{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Anderson Impurity Model ground state solver on Infleqtion's Sqale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ground state quantum chemistry—computing total energies of molecular configurations to within chemical accuracy—is perhaps the most highly-touted industrial application of fault-tolerant quantum computers. Strongly correlated materials, for example, are particularly interesting, and tools like dynamical mean-field theory (DMFT) allow one to account for the effect of their strong, localized electronic correlations. These DMFT models help predict material properties by approximating the system as a single site impurity inside a “bath” that encompasses the rest of the system. Simulating such dynamics can be a tough task using classical methods, but can be done efficiently on a quantum computer via quantum simulation.\n",
    "\n",
    "In this notebook, we showcase a workflow for preparing the ground state of the minimal single-impurity Anderson model (SIAM) using the Hamiltonian Variational Ansatz for a range of realistic parameters. As a first step towards running DMFT on a fault-tolerant quantum computer, we will use logical qubits encoded in the `[[4, 2, 2]]` code. Using this workflow, we will obtain the ground state energy estimates via noisy simulation, and then also execute the corresponding optimized circuits on Infleqtion's gate-based neutral-atom quantum computer, making the benefits of logical qubits apparent. More details can be found in our [paper](https://arxiv.org/abs/2412.07670)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This demo notebook uses CUDA-Q (`cudaq`) and a CUDA-QX library, `cudaq-solvers`; let us first begin by importing (and installing as needed) these packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    import cudaq_solvers as solvers\n",
    "    import cudaq\n",
    "    import matplotlib.pyplot as plt\n",
    "except ImportError:\n",
    "    print(\"Installing required packages...\")\n",
    "    %pip install --quiet 'cudaq-solvers' 'matplotlib'\n",
    "    print(\"Installed `cudaq`, `cudaq-solvers`, and `matplotlib` packages.\")\n",
    "    print(\"You may need to restart the kernel to import newly installed packages.\")\n",
    "    import cudaq_solvers as solvers\n",
    "    import cudaq\n",
    "    import matplotlib.pyplot as plt\n",
    "\n",
    "from collections.abc import Mapping, Sequence\n",
    "import numpy as np\n",
    "from scipy.optimize import minimize\n",
    "import os"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performing logical Variational Quantum Eigensolver (VQE) with CUDA-QX"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To prepare our ground state quantum Anderson impurity model circuits (referred to as AIM circuits in this notebook for short), we use VQE to train an ansatz to minimize a Hamiltonian and obtain optimal angles that can be used to set the AIM circuits. As described in our [paper](https://arxiv.org/abs/2412.07670), the associated restricted Hamiltonian for our SIAM can be reduced to,\n",
    "$$  \n",
    "\\begin{equation}\n",
    "H_{(U, V)} = U (Z_0 Z_2 - 1) / 4 + V (X_0 + X_2),\n",
    "\\end{equation}\n",
    "$$\n",
    "where $U$ is the Coulomb interaction and $V$ the hybridization strength. In this notebook workflow, we will optimize over a 2-dimensional grid of Hamiltonian parameter values, namely $U\\in \\{1, 5, 9\\}$ and $V\\in \\{-9, -1, 7\\}$ (with all values assumed to be in units of eV), to ensure that the ansatz is generally trainable and expressive, and obtain 9 different circuit layers identified by the key $(U, V)$. We will simulate the VQE on GPU (or optionally on CPU if you do not have GPU access), enabled by CUDA-Q, in the absence of noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "if cudaq.num_available_gpus() == 0:\n",
    "    cudaq.set_target(\"qpp-cpu\", option=\"fp64\")\n",
    "else:\n",
    "    cudaq.set_target(\"nvidia\", option=\"fp64\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This workflow can be easily defined in CUDA-Q as shown in the cell below, using the CUDA-QX Solvers library (which accelerates quantum algorithms like the VQE):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ansatz(n_qubits: int) -> cudaq.Kernel:\n",
    "    # Create a CUDA-Q parameterized kernel\n",
    "    paramterized_ansatz, variational_angles = cudaq.make_kernel(list)\n",
    "    qubits = paramterized_ansatz.qalloc(n_qubits)\n",
    "\n",
    "    # Using |+> as the initial state:\n",
    "    paramterized_ansatz.h(qubits[0])\n",
    "    paramterized_ansatz.cx(qubits[0], qubits[1])\n",
    "\n",
    "    paramterized_ansatz.rx(variational_angles[0], qubits[0])\n",
    "    paramterized_ansatz.cx(qubits[0], qubits[1])\n",
    "    paramterized_ansatz.rz(variational_angles[1], qubits[1])\n",
    "    paramterized_ansatz.cx(qubits[0], qubits[1])\n",
    "    return paramterized_ansatz\n",
    "\n",
    "\n",
    "def run_logical_vqe(cudaq_hamiltonian: cudaq.SpinOperator) -> tuple[float, list[float]]:\n",
    "    # Set seed for easier reproduction\n",
    "    np.random.seed(42)\n",
    "\n",
    "    # Initial angles for the optimizer\n",
    "    init_angles = np.random.random(2) * 1e-1\n",
    "\n",
    "    # Obtain CUDA-Q Ansatz\n",
    "    num_qubits = cudaq_hamiltonian.get_qubit_count()\n",
    "    variational_kernel = ansatz(num_qubits)\n",
    "\n",
    "    # Perform VQE optimization\n",
    "    energy, params, _ = solvers.vqe(\n",
    "        variational_kernel,\n",
    "        cudaq_hamiltonian,\n",
    "        init_angles,\n",
    "        optimizer=minimize,\n",
    "        method=\"SLSQP\",\n",
    "        tol=1e-10,\n",
    "    )\n",
    "    return energy, params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constructing circuits in the `[[4,2,2]]` encoding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `[[4,2,2]]` code is a quantum error detection code that uses four physical qubits to encode two logical qubits. In this notebook, we will construct two variants of quantum circuits: physical (bare, unencoded) and logical (encoded). These circuits will be informed by the Hamiltonian Variational Ansatz described earlier. To measure all the terms in our Hamiltonian, we will measure the data qubits in both the $Z$- and $X$-basis, as allowed by the `[[4,2,2]]` logical gateset. Full details on the circuit constructions are outlined in our [paper](https://arxiv.org/abs/2412.07670)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we create functions to build our CUDA-Q AIM circuits, both physical and logical versions. As we consider noisy simulation in this notebook, we will include some noisy gates. Here, for simplicity, we will just register a custom identity gate -- to be later used as a noisy operation to model readout error: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "cudaq.register_operation(\"meas_id\", np.identity(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def aim_physical_circuit(\n",
    "    angles: list[float], basis: str, *, ignore_meas_id: bool = False\n",
    ") -> cudaq.Kernel:\n",
    "    kernel = cudaq.make_kernel()\n",
    "    qubits = kernel.qalloc(2)\n",
    "\n",
    "    # Bell state prep\n",
    "    kernel.h(qubits[0])\n",
    "    kernel.cx(qubits[0], qubits[1])\n",
    "\n",
    "    # Rx Gate\n",
    "    kernel.rx(angles[0], qubits[0])\n",
    "\n",
    "    # ZZ rotation\n",
    "    kernel.cx(qubits[0], qubits[1])\n",
    "    kernel.rz(angles[1], qubits[1])\n",
    "    kernel.cx(qubits[0], qubits[1])\n",
    "\n",
    "    if basis == \"z_basis\":\n",
    "        if not ignore_meas_id:\n",
    "            kernel.for_loop(\n",
    "                start=0, stop=2, function=lambda q_idx: getattr(kernel, \"meas_id\")(qubits[q_idx])\n",
    "            )\n",
    "        kernel.mz(qubits)\n",
    "    elif basis == \"x_basis\":\n",
    "        kernel.h(qubits)\n",
    "        if not ignore_meas_id:\n",
    "            kernel.for_loop(\n",
    "                start=0, stop=2, function=lambda q_idx: getattr(kernel, \"meas_id\")(qubits[q_idx])\n",
    "            )\n",
    "        kernel.mz(qubits)\n",
    "    else:\n",
    "        raise ValueError(\"Unsupported basis provided:\", basis)\n",
    "    return kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def aim_logical_circuit(\n",
    "    angles: list[float], basis: str, *, ignore_meas_id: bool = False\n",
    ") -> cudaq.Kernel:\n",
    "    kernel = cudaq.make_kernel()\n",
    "    qubits = kernel.qalloc(6)\n",
    "\n",
    "    kernel.for_loop(start=0, stop=3, function=lambda idx: kernel.h(qubits[idx]))\n",
    "    kernel.cx(qubits[1], qubits[4])\n",
    "    kernel.cx(qubits[2], qubits[3])\n",
    "    kernel.cx(qubits[0], qubits[1])\n",
    "    kernel.cx(qubits[0], qubits[3])\n",
    "\n",
    "    # Rx teleportation\n",
    "    kernel.rx(angles[0], qubits[0])\n",
    "\n",
    "    kernel.cx(qubits[0], qubits[1])\n",
    "    kernel.cx(qubits[0], qubits[3])\n",
    "    kernel.h(qubits[0])\n",
    "\n",
    "    if basis == \"z_basis\":\n",
    "        if not ignore_meas_id:\n",
    "            kernel.for_loop(\n",
    "                start=0, stop=5, function=lambda idx: getattr(kernel, \"meas_id\")(qubits[idx])\n",
    "            )\n",
    "        kernel.mz(qubits)\n",
    "    elif basis == \"x_basis\":\n",
    "        # ZZ rotation and teleportation\n",
    "        kernel.cx(qubits[3], qubits[5])\n",
    "        kernel.cx(qubits[2], qubits[5])\n",
    "        kernel.rz(angles[1], qubits[5])\n",
    "        kernel.cx(qubits[1], qubits[5])\n",
    "        kernel.cx(qubits[4], qubits[5])\n",
    "        kernel.for_loop(start=1, stop=5, function=lambda idx: kernel.h(qubits[idx]))\n",
    "        if not ignore_meas_id:\n",
    "            kernel.for_loop(\n",
    "                start=0, stop=6, function=lambda idx: getattr(kernel, \"meas_id\")(qubits[idx])\n",
    "            )\n",
    "        kernel.mz(qubits)\n",
    "    else:\n",
    "        raise ValueError(\"Unsupported basis provided:\", basis)\n",
    "    return kernel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the circuit definitions above, we can now define a function that automatically runs the VQE and constructs a dictionary containing all the AIM circuits we want to submit to hardware (or noisily simulate):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_circuit_set(ignore_meas_id: bool = False) -> object:\n",
    "    u_vals = [1, 5, 9]\n",
    "    v_vals = [-9, -1, 7]\n",
    "    circuit_dict = {}\n",
    "    for u in u_vals:\n",
    "        for v in v_vals:\n",
    "            qubit_hamiltonian = (\n",
    "                0.25 * u * cudaq.spin.z(0) * cudaq.spin.z(1)\n",
    "                - 0.25 * u\n",
    "                + v * cudaq.spin.x(0)\n",
    "                + v * cudaq.spin.x(1)\n",
    "            )\n",
    "            _, opt_params = run_logical_vqe(qubit_hamiltonian)\n",
    "            angles = [float(angle) for angle in opt_params]\n",
    "            print(f\"Computed optimal angles={angles} for U={u}, V={v}\")\n",
    "\n",
    "            tmp_physical_dict = {}\n",
    "            tmp_logical_dict = {}\n",
    "            for basis in (\"z_basis\", \"x_basis\"):\n",
    "                tmp_physical_dict[basis] = aim_physical_circuit(\n",
    "                    angles, basis, ignore_meas_id=ignore_meas_id\n",
    "                )\n",
    "                tmp_logical_dict[basis] = aim_logical_circuit(\n",
    "                    angles, basis, ignore_meas_id=ignore_meas_id\n",
    "                )\n",
    "\n",
    "            circuit_dict[f\"{u}:{v}\"] = {\n",
    "                \"physical\": tmp_physical_dict,\n",
    "                \"logical\": tmp_logical_dict,\n",
    "            }\n",
    "    print(\"\\nFinished building optimized circuits!\")\n",
    "    return circuit_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computed optimal angles=[1.5846845738799267, 1.5707961678256028] for U=1, V=-9\n",
      "Computed optimal angles=[4.588033710930825, 4.712388365176642] for U=1, V=-1\n",
      "Computed optimal angles=[-1.588651490745171, 1.5707962742876598] for U=1, V=7\n",
      "Computed optimal angles=[1.64012940802256, 1.5707963354922125] for U=5, V=-9\n",
      "Computed optimal angles=[2.1293956916868737, 1.5707963294715355] for U=5, V=-1\n",
      "Computed optimal angles=[-1.6598458659836037, 1.570796331040382] for U=5, V=7\n",
      "Computed optimal angles=[1.695151467539617, 1.5707960973500679] for U=9, V=-9\n",
      "Computed optimal angles=[2.4149519241823376, 1.5707928509325972] for U=9, V=-1\n",
      "Computed optimal angles=[-1.7301462729177735, 1.570796033796985] for U=9, V=7\n",
      "\n",
      "Finished building optimized circuits!\n"
     ]
    }
   ],
   "source": [
    "sim_circuit_dict = generate_circuit_set()\n",
    "circuit_layers = sim_circuit_dict.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up submission and decoding workflow "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, we define various helper functions that will play a role in generating the associated energies of the AIM circuits based on the circuit samples (in the different bases), as well as decode the logical circuits with post-selection informed by the `[[4,2,2]]` code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _num_qubits(counts: Mapping[str, float]) -> int:\n",
    "    for key in counts:\n",
    "        if key.isdecimal():\n",
    "            return len(key)\n",
    "    return 0\n",
    "\n",
    "\n",
    "def process_counts(\n",
    "    counts: Mapping[str, float],\n",
    "    data_qubits: Sequence[int],\n",
    "    flag_qubits: Sequence[int] = (),\n",
    ") -> dict[str, float]:\n",
    "    new_data: dict[str, float] = {}\n",
    "    for key, val in counts.items():\n",
    "        if not all(key[i] == \"0\" for i in flag_qubits):\n",
    "            continue\n",
    "\n",
    "        new_key = \"\".join(key[i] for i in data_qubits)\n",
    "\n",
    "        if not set(\"01\").issuperset(new_key):\n",
    "            continue\n",
    "\n",
    "        new_data.setdefault(new_key, 0)\n",
    "        new_data[new_key] += val\n",
    "\n",
    "    return new_data\n",
    "\n",
    "\n",
    "def decode(counts: Mapping[str, float]) -> dict[str, float]:\n",
    "    \"\"\"Decode physical counts into logical counts. Should be called after `process_counts`.\"\"\"\n",
    "\n",
    "    if not counts:\n",
    "        return {}\n",
    "\n",
    "    num_qubits = _num_qubits(counts)\n",
    "    assert num_qubits % 4 == 0\n",
    "\n",
    "    physical_to_logical = {\n",
    "        \"0000\": \"00\",\n",
    "        \"1111\": \"00\",\n",
    "        \"0011\": \"01\",\n",
    "        \"1100\": \"01\",\n",
    "        \"0101\": \"10\",\n",
    "        \"1010\": \"10\",\n",
    "        \"0110\": \"11\",\n",
    "        \"1001\": \"11\",\n",
    "    }\n",
    "\n",
    "    new_data: dict[str, float] = {}\n",
    "    for key, val in counts.items():\n",
    "        physical_keys = [key[i : i + 4] for i in range(0, num_qubits, 4)]\n",
    "        logical_keys = [physical_to_logical.get(physical_key) for physical_key in physical_keys]\n",
    "        if None not in logical_keys:\n",
    "            new_key = \"\".join(logical_keys)\n",
    "            new_data.setdefault(new_key, 0)\n",
    "            new_data[new_key] += val\n",
    "\n",
    "    return new_data\n",
    "\n",
    "\n",
    "def ev_x(counts: Mapping[str, float]) -> float:\n",
    "    ev = 0.0\n",
    "\n",
    "    for k, val in counts.items():\n",
    "        ev += val * ((-1) ** int(k[0]) + (-1) ** int(k[1]))\n",
    "\n",
    "    total = sum(counts.values())\n",
    "    ev /= total\n",
    "    return ev\n",
    "\n",
    "\n",
    "def ev_xx(counts: Mapping[str, float]) -> float:\n",
    "    ev = 0.0\n",
    "\n",
    "    for k, val in counts.items():\n",
    "        ev += val * (-1) ** k.count(\"1\")\n",
    "\n",
    "    total = sum(counts.values())\n",
    "    ev /= total\n",
    "    return ev\n",
    "\n",
    "\n",
    "def ev_zz(counts: Mapping[str, float]) -> float:\n",
    "    ev = 0.0\n",
    "\n",
    "    for k, val in counts.items():\n",
    "        ev += val * (-1) ** k.count(\"1\")\n",
    "\n",
    "    total = sum(counts.values())\n",
    "    ev /= total\n",
    "    return ev\n",
    "\n",
    "\n",
    "def aim_logical_energies(\n",
    "    data_ordering: object, counts_list: Sequence[dict[str, float]]\n",
    ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n",
    "    counts_data = {\n",
    "        data_ordering[i]: decode(\n",
    "            process_counts(\n",
    "                counts,\n",
    "                data_qubits=[1, 2, 3, 4],\n",
    "                flag_qubits=[0, 5],\n",
    "            )\n",
    "        )\n",
    "        for i, counts in enumerate(counts_list)\n",
    "    }\n",
    "    return _aim_energies(counts_data)\n",
    "\n",
    "\n",
    "def aim_physical_energies(\n",
    "    data_ordering: object, counts_list: Sequence[dict[str, float]]\n",
    ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n",
    "    counts_data = {\n",
    "        data_ordering[i]: process_counts(\n",
    "            counts,\n",
    "            data_qubits=[0, 1],\n",
    "        )\n",
    "        for i, counts in enumerate(counts_list)\n",
    "    }\n",
    "    return _aim_energies(counts_data)\n",
    "\n",
    "\n",
    "def _aim_energies(\n",
    "    counts_data: Mapping[tuple[int, int, str], dict[str, float]],\n",
    ") -> tuple[dict[tuple[int, int], float], dict[tuple[int, int], float]]:\n",
    "    evxs: dict[tuple[int, int], float] = {}\n",
    "    evxxs: dict[tuple[int, int], float] = {}\n",
    "    evzzs: dict[tuple[int, int], float] = {}\n",
    "    totals: dict[tuple[int, int], float] = {}\n",
    "\n",
    "    for key, counts in counts_data.items():\n",
    "        h_params, basis = key\n",
    "        key_a, key_b = h_params.split(\":\")\n",
    "        u, v = int(key_a), int(key_b)\n",
    "        if basis.startswith(\"x\"):\n",
    "            evxs[u, v] = ev_x(counts)\n",
    "            evxxs[u, v] = ev_xx(counts)\n",
    "        else:\n",
    "            evzzs[u, v] = ev_zz(counts)\n",
    "\n",
    "        totals.setdefault((u, v), 0)\n",
    "        totals[u, v] += sum(counts.values())\n",
    "\n",
    "    energies = {}\n",
    "    uncertainties = {}\n",
    "    for u, v in evxs.keys() & evzzs.keys():\n",
    "        string_key = f\"{u}:{v}\"\n",
    "        energies[string_key] = u * (evzzs[u, v] - 1) / 4 + v * evxs[u, v]\n",
    "\n",
    "        uncertainty_xx = 2 * v**2 * (1 + evxxs[u, v]) - u * v * evxs[u, v] / 2\n",
    "        uncertainty_zz = u**2 * (1 - evzzs[u, v]) / 2\n",
    "\n",
    "        uncertainties[string_key] = np.sqrt(\n",
    "            (uncertainty_zz + uncertainty_xx - energies[string_key] ** 2) / (totals[u, v] / 2)\n",
    "        )\n",
    "\n",
    "    return energies, uncertainties\n",
    "\n",
    "\n",
    "def _get_energy_diff(\n",
    "    bf_energies: dict[str, float],\n",
    "    physical_energies: dict[str, float],\n",
    "    logical_energies: dict[str, float],\n",
    ") -> tuple[list[float], list[float]]:\n",
    "    physical_energy_diff = []\n",
    "    logical_energy_diff = []\n",
    "\n",
    "    # Data ordering following `bf_energies` keys\n",
    "    for layer in bf_energies.keys():\n",
    "        physical_sim_energy = physical_energies[layer]\n",
    "        logical_sim_energy = logical_energies[layer]\n",
    "        true_energy = bf_energies[layer]\n",
    "        u, v = layer.split(\":\")\n",
    "        print(f\"Layer=({u}, {v}) has brute-force energy of: {true_energy}\")\n",
    "        print(f\"Physical circuit of layer=({u}, {v}) got an energy of: {physical_sim_energy}\")\n",
    "        print(f\"Logical circuit of layer=({u}, {v}) got an energy of: {logical_sim_energy}\")\n",
    "        print(\"-\" * 72)\n",
    "\n",
    "        if logical_sim_energy < physical_sim_energy:\n",
    "            print(\"Logical circuit achieved the lower energy!\")\n",
    "        else:\n",
    "            print(\"Physical circuit achieved the lower energy\")\n",
    "        print(\"-\" * 72, \"\\n\")\n",
    "\n",
    "        physical_energy_diff.append(\n",
    "            -1 * (true_energy - physical_sim_energy)\n",
    "        )  # Multiply by -1 since negative energies\n",
    "        logical_energy_diff.append(-1 * (true_energy - logical_sim_energy))\n",
    "    return physical_energy_diff, logical_energy_diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def submit_aim_circuits(\n",
    "    circuit_dict: object,\n",
    "    *,\n",
    "    folder_path: str = \"future_aim_results\",\n",
    "    shots_count: int = 1000,\n",
    "    noise_model: cudaq.mlir._mlir_libs._quakeDialects.cudaq_runtime.NoiseModel | None = None,\n",
    "    run_async: bool = False,\n",
    ") -> dict[str, list[dict[str, int]]] | None:\n",
    "    if run_async:\n",
    "        os.makedirs(folder_path, exist_ok=True)\n",
    "    else:\n",
    "        aim_results = {\"physical\": [], \"logical\": []}\n",
    "\n",
    "    for layer in circuit_dict.keys():\n",
    "        if run_async:\n",
    "            print(f\"Posting circuits associated with layer=('{layer}')\")\n",
    "        else:\n",
    "            print(f\"Running circuits associated with layer=('{layer}')\")\n",
    "\n",
    "        for basis in (\"z_basis\", \"x_basis\"):\n",
    "            if run_async:\n",
    "                u, v = layer.split(\":\")\n",
    "\n",
    "                tmp_physical_results = cudaq.sample_async(\n",
    "                    circuit_dict[layer][\"physical\"][basis], shots_count=shots_count\n",
    "                )\n",
    "                file = open(f\"{folder_path}/physical_{basis}_job_u={u}_v={v}_result.txt\", \"w\")\n",
    "                file.write(str(tmp_physical_results))\n",
    "                file.close()\n",
    "\n",
    "                tmp_logical_results = cudaq.sample_async(\n",
    "                    circuit_dict[layer][\"logical\"][basis], shots_count=shots_count\n",
    "                )\n",
    "                file = open(f\"{folder_path}/logical_{basis}_job_u={u}_v={v}_result.txt\", \"w\")\n",
    "                file.write(str(tmp_logical_results))\n",
    "                file.close()\n",
    "            else:\n",
    "                tmp_physical_results = cudaq.sample(\n",
    "                    circuit_dict[layer][\"physical\"][basis],\n",
    "                    shots_count=shots_count,\n",
    "                    noise_model=noise_model,\n",
    "                )\n",
    "                tmp_logical_results = cudaq.sample(\n",
    "                    circuit_dict[layer][\"logical\"][basis],\n",
    "                    shots_count=shots_count,\n",
    "                    noise_model=noise_model,\n",
    "                )\n",
    "                aim_results[\"physical\"].append({k: v for k, v in tmp_physical_results.items()})\n",
    "                aim_results[\"logical\"].append({k: v for k, v in tmp_logical_results.items()})\n",
    "    if not run_async:\n",
    "        print(\"\\nCompleted all circuit sampling!\")\n",
    "        return aim_results\n",
    "    else:\n",
    "        print(\"\\nAll circuits submitted for async sampling!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _get_async_results(\n",
    "    layers: object, *, folder_path: str = \"future_aim_results\"\n",
    ") -> dict[str, list[dict[str, int]]]:\n",
    "    aim_results = {\"physical\": [], \"logical\": []}\n",
    "    for layer in layers:\n",
    "        print(f\"Retrieving all circuits counts associated with layer=('{layer}')\")\n",
    "        u, v = layer.split(\":\")\n",
    "        for basis in (\"z_basis\", \"x_basis\"):\n",
    "            file = open(f\"{folder_path}/physical_{basis}_job_u={u}_v={v}_result.txt\", \"r\")\n",
    "            tmp_physical_results = cudaq.AsyncSampleResult(str(file.read()))\n",
    "            physical_counts = tmp_physical_results.get()\n",
    "\n",
    "            file = open(f\"{folder_path}/logical_{basis}_job_u={u}_v={v}_result.txt\", \"r\")\n",
    "            tmp_logical_results = cudaq.AsyncSampleResult(str(file.read()))\n",
    "            logical_counts = tmp_logical_results.get()\n",
    "\n",
    "            aim_results[\"physical\"].append({k: v for k, v in physical_counts.items()})\n",
    "            aim_results[\"logical\"].append({k: v for k, v in logical_counts.items()})\n",
    "\n",
    "    print(\"\\nObtained all circuit samples!\")\n",
    "    return aim_results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running a CUDA-Q noisy simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, we will first explore the performance of the physical and logical circuits under the influence of a device noise model. This will help us predict experimental results, as well as understand the dominant error sources at play. Such a simulation can be achieved via CUDA-Q's density matrix simulator: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "cudaq.reset_target()\n",
    "cudaq.set_target(\"density-matrix-cpu\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_device_noise(\n",
    "    depolar_prob_1q: float,\n",
    "    depolar_prob_2q: float,\n",
    "    *,\n",
    "    readout_error_prob: float | None = None,\n",
    "    custom_gates: list[str] | None = None,\n",
    ") -> cudaq.mlir._mlir_libs._quakeDialects.cudaq_runtime.NoiseModel:\n",
    "    noise = cudaq.NoiseModel()\n",
    "    depolar_noise = cudaq.DepolarizationChannel(depolar_prob_1q)\n",
    "\n",
    "    noisy_ops = [\"z\", \"s\", \"x\", \"h\", \"rx\", \"rz\"]\n",
    "    for op in noisy_ops:\n",
    "        noise.add_all_qubit_channel(op, depolar_noise)\n",
    "\n",
    "    if custom_gates:\n",
    "        custom_depolar_channel = cudaq.DepolarizationChannel(depolar_prob_1q)\n",
    "        for op in custom_gates:\n",
    "            noise.add_all_qubit_channel(op, custom_depolar_channel)\n",
    "\n",
    "    # Two qubit depolarization error\n",
    "    p_0 = 1 - depolar_prob_2q\n",
    "    p_1 = np.sqrt((1 - p_0**2) / 3)\n",
    "\n",
    "    k0 = np.array(\n",
    "        [[p_0, 0.0, 0.0, 0.0], [0.0, p_0, 0.0, 0.0], [0.0, 0.0, p_0, 0.0], [0.0, 0.0, 0.0, p_0]],\n",
    "        dtype=np.complex128,\n",
    "    )\n",
    "    k1 = np.array(\n",
    "        [[0.0, 0.0, p_1, 0.0], [0.0, 0.0, 0.0, p_1], [p_1, 0.0, 0.0, 0.0], [0.0, p_1, 0.0, 0.0]],\n",
    "        dtype=np.complex128,\n",
    "    )\n",
    "    k2 = np.array(\n",
    "        [\n",
    "            [0.0, 0.0, -1j * p_1, 0.0],\n",
    "            [0.0, 0.0, 0.0, -1j * p_1],\n",
    "            [1j * p_1, 0.0, 0.0, 0.0],\n",
    "            [0.0, 1j * p_1, 0.0, 0.0],\n",
    "        ],\n",
    "        dtype=np.complex128,\n",
    "    )\n",
    "    k3 = np.array(\n",
    "        [[p_1, 0.0, 0.0, 0.0], [0.0, p_1, 0.0, 0.0], [0.0, 0.0, -p_1, 0.0], [0.0, 0.0, 0.0, -p_1]],\n",
    "        dtype=np.complex128,\n",
    "    )\n",
    "    kraus_channel = cudaq.KrausChannel([k0, k1, k2, k3])\n",
    "\n",
    "    noise.add_all_qubit_channel(\"cz\", kraus_channel)\n",
    "    noise.add_all_qubit_channel(\"cx\", kraus_channel)\n",
    "\n",
    "    if readout_error_prob is not None:\n",
    "        # Readout error modeled with a Bit flip channel on identity before measurement\n",
    "        bit_flip = cudaq.BitFlipChannel(readout_error_prob)\n",
    "        noise.add_all_qubit_channel(\"meas_id\", bit_flip)\n",
    "    return noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, with our example noise model defined above, we can synchronously & noisily sample all of our AIM circuits by passing `noise_model=cudaq_noise_model` to the workflow containing function `submit_aim_circuits()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Example parameters that can model execution on hardware at the high, simulation, level:\n",
    "# Take single-qubit gate depolarization rate: ~0.2% or better (fidelity ≥99.8%)\n",
    "# Take two-qubit gate depolarization rate: ~1–2% (fidelity ~98–99%)\n",
    "cudaq_noise_model = get_device_noise(0.002, 0.02, readout_error_prob=0.02)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running circuits associated with layer=('1:-9')\n",
      "Running circuits associated with layer=('1:-1')\n",
      "Running circuits associated with layer=('1:7')\n",
      "Running circuits associated with layer=('5:-9')\n",
      "Running circuits associated with layer=('5:-1')\n",
      "Running circuits associated with layer=('5:7')\n",
      "Running circuits associated with layer=('9:-9')\n",
      "Running circuits associated with layer=('9:-1')\n",
      "Running circuits associated with layer=('9:7')\n",
      "\n",
      "Completed all circuit sampling!\n"
     ]
    }
   ],
   "source": [
    "aim_sim_data = submit_aim_circuits(sim_circuit_dict, noise_model=cudaq_noise_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_ordering = []\n",
    "for key in circuit_layers:\n",
    "    for basis in (\"z_basis\", \"x_basis\"):\n",
    "        data_ordering.append((key, basis))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_physical_energies, sim_physical_uncertainties = aim_physical_energies(\n",
    "    data_ordering, aim_sim_data[\"physical\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_logical_energies, sim_logical_uncertainties = aim_logical_energies(\n",
    "    data_ordering, aim_sim_data[\"logical\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To analyze our simulated energy results in the above cells, we will compare them to the brute-force computed exact ground state energies for the AIM Hamiltonian. For simplicity, these are already stored in the dictionary `bf_energies` below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "bf_energies = {\n",
    "    \"1:-9\": -18.251736027394713,\n",
    "    \"1:-1\": -2.265564437074638,\n",
    "    \"1:7\": -14.252231964940428,\n",
    "    \"5:-9\": -19.293350575766127,\n",
    "    \"5:-1\": -3.608495283014149,\n",
    "    \"5:7\": -15.305692796870582,\n",
    "    \"9:-9\": -20.39007993367173,\n",
    "    \"9:-1\": -5.260398644698076,\n",
    "    \"9:7\": -16.429650912487233,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the above metric, we can assess the performance of the logical circuits against the physical circuits by considering how far away the respective energies are from the brute-force expected energies. The cell below computes these energy deviations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer=(1, -9) has brute-force energy of: -18.251736027394713\n",
      "Physical circuit of layer=(1, -9) got an energy of: -15.929\n",
      "Logical circuit of layer=(1, -9) got an energy of: -17.46016175277361\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(1, -1) has brute-force energy of: -2.265564437074638\n",
      "Physical circuit of layer=(1, -1) got an energy of: -1.97\n",
      "Logical circuit of layer=(1, -1) got an energy of: -2.176531948420889\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(1, 7) has brute-force energy of: -14.252231964940428\n",
      "Physical circuit of layer=(1, 7) got an energy of: -12.268\n",
      "Logical circuit of layer=(1, 7) got an energy of: -13.26321740664324\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, -9) has brute-force energy of: -19.293350575766127\n",
      "Physical circuit of layer=(5, -9) got an energy of: -16.8495\n",
      "Logical circuit of layer=(5, -9) got an energy of: -18.46681284816878\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, -1) has brute-force energy of: -3.608495283014149\n",
      "Physical circuit of layer=(5, -1) got an energy of: -3.1965000000000003\n",
      "Logical circuit of layer=(5, -1) got an energy of: -3.4531715120183297\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, 7) has brute-force energy of: -15.305692796870582\n",
      "Physical circuit of layer=(5, 7) got an energy of: -13.336\n",
      "Logical circuit of layer=(5, 7) got an energy of: -14.341784541550897\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, -9) has brute-force energy of: -20.39007993367173\n",
      "Physical circuit of layer=(9, -9) got an energy of: -17.802\n",
      "Logical circuit of layer=(9, -9) got an energy of: -19.339249509416753\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, -1) has brute-force energy of: -5.260398644698076\n",
      "Physical circuit of layer=(9, -1) got an energy of: -4.8580000000000005\n",
      "Logical circuit of layer=(9, -1) got an energy of: -5.1227150992242025\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, 7) has brute-force energy of: -16.429650912487233\n",
      "Physical circuit of layer=(9, 7) got an energy of: -14.3635\n",
      "Logical circuit of layer=(9, 7) got an energy of: -15.448422736181264\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n"
     ]
    }
   ],
   "source": [
    "sim_physical_energy_diff, sim_logical_energy_diff = _get_energy_diff(\n",
    "    bf_energies, sim_physical_energies, sim_logical_energies\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both physical and logical circuits were subject to the same noise model, but the `[[4,2,2]]` provides additional information that can help overcome some errors. Visualizing the computed energy differences from the above the cell, our noisy simulation provides a preview of the benefits logical qubits can offer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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odNvn7Aoik8kKVHFPREQEhg4dCkEQRNdNmTIFq1atgomJicbzlCtXDnv37sXKlSu1Mh5RUbBnzx5RrF69epg0aZJWxq9evTr69u2rlbGIiDS1dOlSucuGhoYYMGCAnrIhIiL60NW0V69ecrGbN2/i7NmzesqIiOjzxGIQIiKiQurJkyf43//+J4obGhpiz549qFChglbnK1OmDE6ePInevXtrddyiqF27djh8+DBMTU1F112/fh0rVqzQeI5nz57h1KlTovjAgQNRrlw5yZbQBbk7SGRkJKZMmSJ53fr161G9enWN56hSpQo2btwoed348eORkJCg8RzaIggC1q9fL4oPHDgQACR/3C/I9+9HPj4+okIWdfNOT08XFZL4+fmhfPnyauenbT/88INkx5b27dtjzpw5Wp9vxIgR+O+//2BnZ6f1sYkKk2fPniEkJEQUHzp0aIHqHEREpA1hYWGiA2tNmjSR7IpHRESUn7p16yaKSf3WQUREumOk7wSIiIhIPVOnTkV6erooPnnyZHh7e+tkThMTE4wYMUInYxc1Pj4+WLx4Mb7++mvRdb/88gu++uormJubqz3++vXrRd0GateujRo1agD4UDSQs1hk69atWLhwoWSRir7Nnz9fshijW7du6Nixo9bmadeuHXr06IGdO3fKxSMjI7FkyRL8/PPPWptLE2fPnhUtl2NsbJxdjNW/f39Mnz5d7jFw9+5dXLt2DXXr1s3XXFU1ePBg/PTTT9mX1c374MGDoiVmcnYe0afg4GDJ4iNHR0esWbNGZ/P6+PjobGx1hIWF4c6dO3j27Fn2c9ze3h5NmjRBtWrVVBorOjoat27dwtOnTxEdHY3379/DzMwMNjY2KFu2LKpUqQIXFxce7M8HgiAgNDQUQUFBiIiIQHx8PN6/fw9zc3NYWFjA2dkZrq6uqFixomRHJl17/vy5ZLx27dr5m4ie3Lt3D0FBQXj9+jWSk5NhY2MDV1dX1K9fX+WDwykpKbh58ybu37+fvexO8eLFUalSJdSvXx+Ghoa6+BOKjPT0dDx58gQhISF4+/YtEhISkJaWBjs7Ozg4OKB06dKoW7euRp8JC7uMjAzcvn0bDx48wJs3b5CcnAwTExPY2dmhQoUK8PT01MvryP379xEUFIRXr17h/fv3sLe3h7OzM7y8vODi4pLv+eRm06ZNou8FXbt21VM2uUtMTMT169fx5MkTREVFITU1FWZmZihWrBjc3NxQp04dtZbx+lwkJyfj5s2bePLkCSIiIpCSkgI7OzsUL14cZcqUgZeXF4yM8vfn/levXuH27dsICwtDfHw8MjMzYWtrCy8vL9SrVy9fc9FEQkICgoKC8PjxY8THxyM+Ph6GhoawsLCAtbU1ypYtC1dXV5QvX75QvPe9f/8e169fR0hICKKiopCeng47Ozu4ubmhfv36sLGx0XkOcXFxuHnzJkJDQxEdHY3U1FQ4ODigWLFicHV1RZ06dWBgwHOVc4qIiMj+zhMTE4OMjAw4OTllv06q+h1KG0JCQnDv3j28ePECiYmJMDQ0hIODA1q1apXne6Kfnx8cHR0RFRWVHdu9ezeWLVsGCwsLXadOREQAIBAREVGh8+LFC8HQ0FAAIPfP1dVVSEtL02tu69atE+UFQAgLC9PqPC4uLqI5Bg4cqPT+UjlOnz5dqzkKgiDUr19fcq41a9aoPWZWVpbg6uoqGnPx4sXZ2yQmJgpWVlaibXbs2KGFv0q7EhMTBRsbG1GuFhYWwqtXr7Q+3+vXrwVLS0vRfM7Oznp//nw0YMAAUX4dO3aU28bPz0+0zahRo7Qyv6bPj+nTp4v2b9SokSAIghAeHi4YGBjIXff111+rnGP79u3lxrCxsRGSkpIEQZB+fdDF8zs3I0aMkLwdV69ena95SJG6f5S9fQICAkT7+vr6ym0TEREh/PLLL0KFChUkbwNV5gsPDxemTZsmVK9eXeFYOZ/HvXv3FrZt2ya8f/8+z/Gl3rNUeS+RIpWXsnx9fUX7BgQEqDSXuv+UcebMGWHw4MGCnZ2d0uNWrFhR6Nu3r7BlyxYhPj5e6dtCE7t27ZLM5eHDh/kyvxRdP++ioqKEadOmCaVLl1Z4XxgaGgpt27YVrl27luecd+/eFfr16yf5WeLjP0dHR2H8+PFCbGysGreIZreJlLCwMNF4Li4uSu8v9d6h6ufXzMxM4fTp08KUKVOEhg0bCsbGxnk+R4yNjYUGDRoIS5YsEZKTkzX+m9X9l9ttpe37ShAE4dixY0K3bt0ECwuLXPOSyWSCl5eXsGTJEiExMVHt+ZR5vY+NjRXmzJkj+Vj49F/lypWF33//XUhNTdXoNtCWL774QpRjeHi42uOp+l6Ul9TUVOGvv/4SmjRpIvkd9tN/JiYmQtu2bYU9e/YIWVlZKs1z9+5d0Xg1a9ZUaYzk5GTB1NRUK+8hXbp0EY2xf/9+lcYQBEFISUkR1qxZI/j5+QlGRka53n62trZCt27dhOPHj6s8z0fKvJYmJiYKixcvzvXzmaafp3Kjrc9vUVFRwuLFi4W6desKMplMqddKS0tLwdfXV5g6dapw69Yt7f9xuVDmtfjWrVtCnz59JL/vfvxnZGQktGvXTjhz5ozWc4yNjRUWLVokeHt7i77z5fzn7OwsDBgwQLhy5YpKc0i9Rqn779PXtrxe+1X5p+rnhzdv3ggzZ85U6jtP2bJlhREjRggPHjxQaY5PKfMcevbsmTBp0iShVKlSCnNZt26dUvMNHDhQtO/WrVvVzp+IiFTD0ksiIqJC6O+//0ZmZqYoPnz4cBgbG+shI1JkxowZkvENGzaoPWZAQACePn0qFzMyMkKfPn2yL1taWkqeEVgQlxLZtWsX4uPjRfEePXqgZMmSWp+vRIkS6NGjhygeERGB/fv3a30+VSUkJGD37t2ieM6lYT4uGfOpbdu24f379zrLTRvKlCmDFi1ayMW2bduG1NRUpcd48+YNjhw5Ihfr2bNngTmzKDk5GVu3bhXF7ezs0K9fPz1klH82b96MypUrY/r06QgNDVV7nKioKIwaNQrly5fHzJkzcffuXaX2i4iIwLZt29C7d2+ULl0aAQEBaudA/+f58+fo0KEDfH19sW7dOsTGxiq975MnT7Blyxb07dsXzs7OukvyE1lZWZLxnN2Eiop///0X7u7umDlzJl6+fKlwu8zMTBw+fBje3t6YPXu25Dbp6en47rvvULNmTWzevBmJiYkKx4uKisLixYvh7u6OS5cuafx3FGaCIGDcuHEoU6YM/Pz88L///Q8XL16U7OKXU3p6OgIDAzFu3Di4uLjotHtUQXD//n34+PigVatW2L17N5KTk3PdXhAEXL16FePGjUP58uUVLvmnqcOHD6NKlSr46aef8OzZs1y3ffDgAb799ltUq1ZNckmq/PTw4UM8fPhQLubm5oYyZcroKSN5Bw8ehJubG4YOHYqzZ89Kfof9VFpaGg4fPoyuXbuidu3auHz5stJzVatWDSVKlJCL3blzR3LJPkUuXLig8DPpyZMnlR4nKytL9BnE0NAQvr6+So8hCALWrVsHV1dXDBs2DKdPn0ZGRkau+8TFxWH37t1o2bIl2rZtiwcPHig9n7KOHz8Od3d3jB8/XunPZwXRX3/9hS+++ALjx4/HtWvXRN11FElKSsKZM2cwa9Ys1K5dG/PmzdNxpsrJzMzEDz/8AA8PD2zduhVJSUkKt83IyMDBgwfh6+uL/v37S34XV1VGRgYWLlyIcuXKYcKECbhy5YrCz2MfRUREYOPGjahXrx769u2LV69eaZxHYZOcnIwff/wRrq6umDZtmlLPqfDwcKxatQrVqlXD2LFjERcXp/W8fvvtN7i7u2PhwoVauV/8/f1FsYMHD2o8LhERKYfFIERERIXQP//8I4oZGxtj6NChesiGctOyZUu4urqK4oGBgYiMjFRrzL///lsUa926taj1u1SxwPHjx3M9UKQPe/fulYx/9dVXOptT0XNlz549OptTWTt27BAdGHFwcEC7du3kYt26dYOlpaVcLDY2Fvv27dN1ihrLuZxLTEyMSnlv3LhR9GN4QVoi5sSJE5LLHg0YMKBILwUwY8YM9O/fP3spCXWdPXsWNWrUwMqVK/M86JGbqKioPA/oUd6Cg4PRoEEDHDhwQOOxVCn60oSTk5NkvCgWB61cuRKdO3dW6WBnVlYWpk6diqlTp8rFU1JS8OWXX2LhwoV5HsD51Js3b9CqVStcu3ZN6X2KmszMTCxduhSvX7/WaJyIiAgMHz4cI0eOVKqQpLDZtWsXvLy8cP78ebX2j4iIwMCBAzFo0CCt3j7Lli1D+/btVb7/Hj9+DB8fHwQFBWktF1XlLI4FPrTk1zdBEPD999+jffv2CpfuyktQUBAaN26MP//8U+l9mjZtKsoj59KZucmt4EOVYpCbN28iJiZGLubp6QlbW1ul9o+Pj0fnzp0xZMgQvH37Vul5P3XkyBHUr18f586dU2t/KX/99Rfatm2LFy9eaG1MfZgwYQK++uoruWUr1FUQCvEzMjLQtWtX/Prrryq9fwMfCrl9fHzw5s0bted//fo1fH198d1336lVWCIIArZu3Yr69esjODhY7TwKmwcPHqBu3bqYN2+eWo+jjIwMLFu2DD4+PlorpBEEAUOGDMGkSZOQkpKilTEB8WszABw7dkzlxysREamHxSBERESFzOvXr3Hr1i1R3M/PT+V14En3ZDIZOnXqJIpnZmbi7NmzKo8XFxcnWQwkVfjh5+cnWr81KytLo64k2paeni75A62rqysaNWqks3kbNWokWaRz4sQJvf8gIVXs07t3b5iYmMjFrKys0KVLF6X2L2g6deoEe3t7uZgqXWtybuvu7o4GDRpoJTdtkDowA3zoXlJUrV69Gr/88oso7uzsjNq1a6Np06aoVq1anuuT79u3Dy1btsz1gJytrS2qVq0KX19fNG7cGNWqVRMVRpF2JCUloXXr1gp/YDYwMEDZsmVRv359NGvWDE2aNEHt2rVRunTpfM5U3hdffCEZ/+OPP9QuxCyI9u/fj9GjR4vetypUqICGDRuiSZMmqFixosL9Z8+ejWPHjgH48Pmge/fuOHHihNw25ubmqFatGvz8/ODt7Q0HBwfJseLj49G3b998K/gpTExMTODm5oa6devC398fjRs3RvXq1WFqaqpwn1WrVuG7777Lxyx1b/v27ejVq5fCTiCmpqaoXLkyfH19UadOHTg6Oioca8OGDejZs6dWPrNt2rQJ33zzjWissmXLwtvbG02bNkWNGjUUdl+MjIxEnz59kJaWpnEu6vj4HP6Uj4+PHjKRN2bMGCxYsEDh9ba2tqhZs2b25wNF7+MZGRkYPXo0fv/9d6XmbdasmSimShFHbtsGBAQo3T1Cahyp3KTExMSgWbNmuXYsdHR0RO3ateHv7w8vLy8UL15ccrvY2Fi0bNkS//33n1Jz5+bIkSMYMWKEqLuLvb199n1Zq1atXJ+7BcGyZcuwePFihddbWVmhZs2a8PHxQfPmzVGvXj1UqVKlQBd0jx8/XvLx4uLigoYNG6Jhw4ai3wU+FRQUhDZt2kgWs+fl+fPnaNy4MS5evKhwmxIlSsDDwwP+/v7w8PBQ+FkiPDwcjRs31muBXX65desWGjVqlGvxS9myZeHl5QV/f3/UqlUL1tbWktvduXMHDRs21MpJPz/99JPk9/JSpUrB09MTfn5+cHd3V/m7V9myZVG+fHm5WFRUFK5evapRvkREpBwjfSdAREREqlHUKtfb2zufMyFl+fv7S/6Aef36dcmD+bnZvn276AwNe3t7tG/fXrStTCZD//79Ra3g169fjylTpqg0r67cvXtXsgV9/fr1dT53vXr1RMvtREVF4dGjR6hcubLO55fy4MEDBAYGiuI5l4j5aODAgdi0aZNc7OTJkwgPD0fZsmV1kqM2mJqaok+fPli+fHl27MSJE3jx4kWebc0DAwNFLdkLUlcQAJLLJRgZGaFOnTp6yEb3nj9/jvHjx2dfNjExwZgxYzBgwADUqlVLbtusrCz8999/kgdTLly4gF69ekkeTLa0tMSYMWPQpUsX1K1bFwYG8uc1ZGVlITg4GKdPn8b27dtx4cIFpQ/YFGafvl4cOnRI9Hrftm1bUfcHVcyZM0fyjO769etjwoQJaNmypcKznOPi4hAUFIRjx47hwIED+frDfpkyZVC5cmVRe/x3796hRYsW2L59u95e57Xl7du3GDJkSPYBbAcHB0yZMgW9evUSFeOEhYVh9uzZksWC48aNw/379zFnzhwcOnQoO16/fn389NNPaNasmdwBsMzMTJw8eRITJkzAvXv35MZ6+PAhFi5ciJ9++kmbf2qhY2VlhRYtWqB9+/bw8vKCu7s7jIzEP7+lp6fjxo0b2LBhA/7++2/Ra9+SJUvQrFkzyc94H5UsWVLudWDt2rX466+/5LYZOnSoUt3WcitO0dTDhw8xdOhQyeINNzc3TJ06FZ06dZI70CUIAi5cuIClS5di165dov327t2LBQsW4IcfflA7r/v372Pnzp3Z7xcODg74/vvv0bNnT1HRcHx8PLZu3Ypp06aJOvHcu3cPCxcu1Mvna6nPHDnfe/Pb5s2bFXbzaNGiBSZOnIhmzZrJPS/ev3+Pw4cPY86cObhx44Zov0mTJsHb2xsNGzbMdW5NikHi4uIk5/4oKioKt27dUurznFSxuzLFIIIgoH///pKdlmxtbfH111+jd+/eqF69OmQymdz1t2/fxvLly0VLyr5//x59+/bFnTt31D55JDExEYMHD84e18DAAAMHDsTw4cPh7e0t+lx28eLFAteNEvhQvCX1HmVpaYnRo0ejT58+Cp8/WVlZePz4MS5duoQDBw7g2LFjahVPaNupU6fkur+YmZnhu+++w+DBg0UH30NDQ7F+/XosWLBA1Ini1q1b+O6777By5Uql505NTUWnTp0kl4YsUaIExo0bh65du8LNzU3uuqysLFy5cgULFy4UdeaMjo5Gr169cP36dYUFOH/++Wd2B5LXr1+LflMpUaKEwu6jOVWtWjX7/3v37s1+L75x4wZGjx4tt22dOnWU7lSU23K30dHR6NChg2RnmooVK2LChAno0KGD6Htxeno6zp49i//973+i15hnz55hwIAB+O+//0SvDcq6cuWK3Gdna2trTJo0Cb179xbdh+np6Thw4ABKlSql9Pi1atVCWFiYXCwwMBD16tVTK18iIlKBQERERIXKtGnTBACif/v27dN3aoIgCMK6desk8wsLC9PqPC4uLqI5Bg4cqPT+UjlOnz5dqzl+9OzZM8n5OnbsqPJY3t7eonFGjhypcPuHDx9Kzn327FkN/iLt+fvvvyXzW7hwoc7nXrBggeTcW7du1fncinz//feifNzd3RVun5mZKZQtW1a0z8yZMzXKQ9Pnx/Tp00X7N2rUSG6ba9euibaZM2dOnmN/9dVXcvsYGhoKr1+/lttG6vVBV8/vnFJTUwVjY2PR/LVr186X+ZUhdf8oe/sEBARIPj4+/qtYsaLw4MEDlXOKiYkRSpcuLTlm+/btRfdxXh4+fCgMGTJE2LJlS67bSb1nqfJeIkXqb1CWr6+vaN+AgACl9tX235KVlSWULFlSNObYsWOFzMxMlce7evWq0LdvX7XzUdXcuXMVPk6NjY2FPn36CMePHxfS0tLyJR9dPu8aNmwoREZG5jmOove9efPmCSYmJgIAQSaTCfPmzctzrPj4eMHLy0s0VtmyZZV+fGhym0gJCwsTjefi4qL0/lLvHcp+fk1PTxfc3d2FVatWCcnJySrn/uDBA6FmzZqi+atWrarSONq+TbUxbnp6uuRjBYAwZMgQpW6vnTt3CqamppLP5Rs3biiVh6LvKB//+fv7C9HR0XmOExoaKpQrV060f5kyZdR6bdTEo0ePJG+T1NRUjcbV5L3o6dOngq2trWh/AwMDYcWKFXnun56eLvl5GIBQvnx5IT4+Ps8xypcvr9Zzed++fXL7yGQy0d+yYMGCPMdJTU0VLCws5PYzNTUVUlJS8txX0et069atlXqdFwRBuHDhguDo6Cgao3379krtL/Va+uk/Jycn4dKlS0qNpSvqfuZZsWKFaD9nZ2fh3r17KueQkJAgLF26VFi3bp3qf4CapF6LP/1XoUIFISQkJM9xgoODJZ8nMplMOHPmjNL5jB49WjKPgQMHCklJSUqNsXfvXsHc3Fw0xtixY5XaX9P3fkWkPnv5+vpqPK4gCEL79u0lb/sffvhBSE9PV2qMP//8UzA0NBSN89tvvym1f17viV5eXip//8qL1G+Zffr00eocREQkjcvEEBERFTJSZ10AKLJnnBcF5cqVkzyrJTw8XKVx7t+/jytXrojiirpGAB/OtpQ6g06VJTl06cmTJ5JxDw8Pnc/t6ekpGX/8+LHO55aSmZkp6vIB5H7/GhgYoH///qL4+vXrC3xXBE9PT9SsWVMutn79+lz3SU5Oxo4dO+Ribdq0QYkSJbSdntrCw8ORnp4uin8Or9GlSpXCuXPnFC7RkZtp06ZJnkE6ePBg7N27V+X72M3NDX/99Rf69Omjci70QVBQkGi5ngoVKmDx4sWiM4CVUbduXWzevFlb6eVpzJgxCh836enp2Lp1K1q2bAlHR0e0bNkSU6dOxb///qu1NdfzS506dfDff/8p1ZZ/0qRJaNKkiSg+efLk7CUu5s+fr1SnBWtra2zYsEHU8SI8PFzyjPiizsjICPfv38fw4cPVWkrgiy++wKlTp1ChQgW5+P3790VL9xQ2mzZtkmwD37t3b6xdu1ap26t79+7Ytm2b6LUnPT0dEydO1DjHpk2b4ujRo6Il7KSUL19e8nP0ixcvtLIUhyqkuli4ubmJlhbMT9OmTUNcXJwo/ueff2LkyJF57m9kZIT58+fLdRz7KCwsLNflPT5StztIzm1q1qyJVq1aqTzOpUuXRMshNWzYEGZmZrnuFxYWJtldpkePHjh8+LDSy680bNgQJ0+eFM134MABXL9+XakxFLG0tMSZM2cK7Zn8UssqzZ8/X647hLKsrKwwduxYDBo0SAuZaa5YsWI4ceKEUp3P3N3dceLECVGnGEEQJJ97Us6fPy/X5fGj7777DuvXr4eFhYVS43Tq1An//POPqJvFypUrc102srDasmULDhw4IIr/8ccfmDdvnmQnMSmjRo2S7FIyd+5cUdcXVdWsWRMnT57U+nfsGjVqiGJSXZCIiEj7WAxCRERUyLx48UIy7uTklM+ZkCqk2meqesBJqr37F198gQYNGuS638CBA0WxXbt2ISkpSaX5dUFR+2BF615rk6I2yYqeY7p25MgR0Q9eioo9PiV1/4aGhuLs2bNazU8Xci7v8ujRI5w/f17h9rt27RK1Yy5oS8R8zq/RK1asyLUlsiIvX76UbEnt5eWF1atXw9DQUBvpkYqkChZbt25daO4PKysr7NmzJ8+lLxISEnDixAnMnj0bHTt2ROnSpVGqVCl07twZixcvxvXr1yWXtigIjI2NsXXrVpWKD3I7yNO0aVNMmjRJ6bGqVKmCNm3aiOKftqv/nKjblv0jR0dHyWUFt2zZotG4+vbHH3+IYqVLl8bq1atVus06d+6MESNGiOIBAQG4e/eu2vnZ2dlhy5YtMDY2Vnoff39/NGrUSBS/cOGC2nmo49GjR6KYPpcJjIiIEBXtAkDHjh0l77vc/Prrr5IHDleuXClZdPspf39/UUydYpBmzZqJCkvOnTuX5/xSc0nllNPixYtFY1erVg0bNmxQ+fWlVq1amDt3rigu9Rqjiv/9739qFU4UFFKfbdq1a6eHTLTv999/FxUU5qZixYqSxVU3btyQPAElp19//VUUa9GiBebPn690Dh+1bt0a33zzjVwsPT1d6SVZChOp223o0KGiJWmUMXz4cHTs2FEuFhkZqdHnBiMjI6xbt05u2TZtkXp/CgsLK7Cfs4mIihIWgxARERUyMTExopixsbHSZ16QftjZ2YliqhRjZGRkSJ5RnVehAPDhbLKcZ4YlJiZi586dSs+vK9HR0ZJxW1tbnc8tdZ8AH35A0QepYp+mTZuK1grO6YsvvkD9+vWVGq+g6du3r+jgS25da3Je5+TkhPbt2+skN3VJvUYD+fOY1idPT0906NBBrX3Xrl0rOvhhYGAg2XWA8s/Htdg/ZWNjo4dM1NewYUMcPHhQ5WKs169fY9++fZgwYQLq1q0LFxcXTJ48GQ8fPtRRpurp0aMH3N3dVdqndevWCg96T506VeUDjjkPQgDS3QpIOW3bthU9XgMDA/WUjeYCAwNx8+ZNUXzu3LmwsrJSebw5c+ZIvp9KnZ2urJEjR6pVyNijRw9RTNOuC6p6+vSpKFa6dOl8zeFTa9euRWpqqlzM0NBQqW4eORkZGUkWLrx+/Rr//PNPrvtKFV7k1bHozZs3uH//vlxMqhgkKSkJly5dynUsqbmkupV8Kjo6WvKz+8KFC/PsKKLIyJEjRcXvO3fuVPuEgBIlSuDrr79Wa9+Coih8tpHi7e2N3r17q7xfnz594OXlJYqvWrUq1/1CQkJw8OBBuZihoSEWLVqkdmHk5MmTRV2NCsP3WVUcO3YMQUFBcjFra2v873//U3vMadOmiWKa3G4dO3bUWZdWqd810tPTFZ4gRERE2sNiECIiokImJSVFFCvqBxmLAqmzdqXuS0UOHTqEt2/fysVkMplSxSB2dnaSB2sKwlIxim4DRYUa2qToeaPK/aItERERoh/UAOmuH1Kkttu9e7eoi0ZB4+zsLDobT9GP1E+ePBF1O+nXr59KZ/LmB30+pvVp6NChau+7a9cuUaxNmzaoUqWKJimRhqQes8qcKVrQNG/eHDdv3kTPnj3VPkDx4sWL7DbyX331VYFZSmbIkCEq72NmZia5lJOLiwuaNm2q8ng5l/sCUOCKZgoTQ0ND0UGYR48eKSyeLeiklmSws7OTLKRQhr29veS+UvMoS933L6nlBqU6dejS8+fPRTGpboT5Rep+aNGiBcqXL6/WeP7+/pKvV3nd38WLF0f16tXlYm/fvs21g0zOAg5jY2M0adIEFStWRLly5eSuy63LSFJSEi5fviwXs7a2ljzg/qkDBw6IPv+6ubmhdevWue6XGzMzM3Tr1k0ulpaWJspPWQMGDCj0RbpF5bNNTup8Hsht36NHj+a6z44dO0RLkvr7+4ued6ooUaIEmjdvLhd79eqVwmWSC6Pt27eLYr169VLYsVQZHh4eom49165dU3upGE2+0+WlRIkSkp/Fpd7LiIhIu1gMQkREVMhkZGSIYnm1QCf9k2p9qcpBKamzO3x9feHi4qLU/gMGDBDFzp07h8ePHyudgy5kZmZKxvPjMa1ojrS0NJ3PndPmzZtFnRGsrKzQpUsXpfbv2bOn6O9JTk6WbNVd0ORc5iUxMRG7d+8Wbbdu3TrRj44FbYkYQPo1Gij6r9PqHEQGPpzhe+/ePVFclz9EknKqVasmip06dQobNmzQQzaaKVOmDLZv346goCAMHz4cDg4Oao2TmZmJv/76C9WrV8eJEye0nKVqjIyMJLtCKUPqs4PUkhfKcHV1FcXi4uLUGos+yHlQSBCEQnswTKqrSadOnTR6T+zbt68oFhYWJiqaVkbJkiVRqVIltfKQ2i+/H/uxsbGimDodV7QhIyMDV69eFcV79eql0bh9+vQRxZTplqPqUjE5r/P29s6+LXN29chtnLNnz4o+0zdp0iTPIgqp5R27du2a6z7K8PHxEcUuXryo1ljqftYrSKQ+24wbN05hZ7/CQCaTiYp+VNG9e3dR7NWrV7kunVoYHq8FUX7dbmlpabh27ZrK4xgYGKBJkyYa56OIoaGh5ElSUu9lRESkXSwGISIiKmSk2sTyR/eCL2fLZEC6W4iUt2/f4vDhw6K4sl0jAKBVq1YoUaKEKK7v7iCK2h5LtfDVNkVzWFpa6nzunKTuh65duyqdi729veRyKfq+f5XRpk0b0WMzZ95ZWVnYuHGjXMzT01PyjHR9U/SYLsqv01ZWVpJn7ipDUUt9qR+DKX+5uLhIHjQZNGgQevXqlWeb/IKoevXqWLVqFV6/fo3Dhw/ju+++Q7169VTuMBQTE4M2bdpInuGZX1xcXNReIlBqHXh1O/FIjVWUX+9UkZiYiF27duHHH39Eu3btUKVKFZQqVQrW1tYwMDCATCaT/Ce1LGBhPFAiCIJkB4J69eppNK6XlxcMDMQ/Z6qznI4mHaiklpbI78d+cnKyKKbs9wttu3PnjmQ+mt7fUkVvDx48yPPgvdSyLLkVceTsDPLp/jnHunz5ssKlVqTmyGuJGED6IHHdunXz3C8vUgV7OZepUJZUN5zC5ssvvxTFbt68ierVq2PZsmWF8rW2fPnycHR0VHt/R0dHyceJoo4p6enpkp8BC9rjtaB5+fKlZGFnQbrd3N3ddf5biNRnV3WXriIiIuUV7t5uREREnyGpL2eJiYnIzMyEoaGhHjIiZURFRYliyp65t2nTJlG3AUtLS5XOADI0NETfvn3x22+/ycU3btyIWbNmSf6o/lF8fLxoDW1lVaxYEc7OzgqvV3QgKzY2Vu0zt5Wl6Me+/F43+tq1a7hz544orkqxz8ftc3bUuHjxIh4+fKj2gfr8YGRkhP79+2PBggXZsbNnzyI0NBQVKlQAAJw4cQLh4eFy+xXEriCA4mKionxwtFSpUrm+huRGqqV+hQoV4OTkpGlapAU//fST5FnZO3bswI4dO+Di4oK2bduiSZMmaNy4seRa4AWRiYkJ2rRpgzZt2gD4ULAZFBSEGzdu4Nq1azh37hwePHiQ6xiZmZkYMmQIKleujDp16uRH2nI0eY+UKlpTdzypsdRtTV5U3L17F3PmzMG///4reXBcHYXxAGVcXJzke5+mzxcLCwtUrlwZwcHBcnF12sxr8jySKrrI78e+1ONLUVGqrj179kwUs7Cw0PgzqNTjRRAEhIeHw97eXuF+vr6+MDQ0lOtCeObMGcnvzKGhoXj69Klc7NMCjpxdRtLT03H27Nns95BP5SwqyTmWlNTUVMlujcnJyRoXXko9L9RZdsrExCTX73SFRefOnVGlShXR68erV68wduxYTJgwAX5+fmjevDl8fHzg4eFR4Lv71apVSytj5HwOSD2ngQ/PF6nXnpiYGI0fr1IdngrrMmk5SS1TZWVlhUePHmm8xJjUZwR1brf8+Bwv9d6prc9KRESkGItBiIiIChmp7g7Ahx9cdX3wnNT35s0bUUzZNb2lujt07txZ5TbQAwcOFBWDvHjxAsePH891PeobN26o3RZ43bp1GDRokMLrFT2e8+Ogh6KD8/ldDCJ1/5YrVw5+fn4qjdO6dWsUK1YM7969k4v//fffmDdvniYp6tzgwYPlikEEQcD69esxc+ZMAOJlkkxNTSUPUBcE+nxM64utra3a+758+VIUKywFBZ+D3r1748SJEwq7DD179gwrVqzAihUrAAClS5eGr68vmjZtipYtW6JcuXL5ma7aTE1N4eXlBS8vL4wYMQLAhyWMdu3ahdWrV0suZQQAKSkp+Prrr9XqSKApdbuC5Nd4n6OMjAxMnjwZS5YsUbhkmLoK41mzijo3lCxZUuOxS5UqJTqYq84yD/roBqdNUl2NtP3YU5bU7V+8eHG1i0U/KlasGIyMjER/V173t62tLTw9PeW6G8THx+Pq1auibiM5u3lYWFjIbVOyZElUrVpVrjj+5MmTomKQqKgo3Lp1Sy7m7OyMGjVq5Jqr1EkDgPQyn9qgzkFiTT7rFSSGhobYuXMnGjZsiISEBNH16enpOHHiRPZScCYmJvD09ETTpk3h7+8PX1/fPJf8yW85lxbT1hiKnmOKHq8tWrTQOA8pRaUYROp2S0xMRIMGDXQyX0F9nudcRguQfi8jIiLt4jIxREREhUzZsmUl42FhYfmciWoEQSjQ4+nS06dPJc8UVHRffury5cuSXTlU7RoBADVq1JA8u06fS4koug00PTtGGQ8fPpSMly9fXudzf/T+/Xts27ZNFO/fvz9kMplKYxkZGaFv376i+KZNm+TOiiyIqlSpImojvmHDBmRlZSE6Ohr79++Xu65Tp065ng2qT4X1NVoTmhxETkxMFMXs7Ow0yIa0be3atfj555+V6j728uVLbN26FcOGDYOrqyuaNGmCDRs26O3gpCZKliyJb775Bnfu3MGGDRsUFgpeunQp+6ARfb7S09PRo0cP/Pbbbzp5vBemz70fKTqQqI2iW6kDVuoUgxR2Uu+/KSkpeshE+vbXVoG11DjK3N9SHTn+++8/USxnMYiPjw9MTExyHUtqnICAANFztWnTpnl+ps/vg93qdKsrSgWD1atXR2BgINzd3fPcNi0tDYGBgfjf//6H5s2bo2TJkhgzZky+fFdVVn6/phaGx2tBVBhut/x4nkt1ASnshZlERIVBwSplJSIiojxVq1ZNMn7lypUCsY6vojaq2m79KHWGpL7aIucl5xliH1WvXj3PfXN2RAA+/OBjYWGhVhvW+vXr4+bNm3Kx/fv3IyYmRi8H1xU9nq9evYqePXvqdO6rV69KxhXlpAt79+6V/KGtcuXKat2/VatWFcVevXqFY8eOoW3btmrlmF8GDx6My5cvZ19+/vw5Tp06hZCQEKSmpoq2LaicnZ0lO7Qoerx97qQKlaTaB5P+GBgYYNasWejbty9mzpyJf/75R/SclCIIAs6dO4dz585h1qxZ+PPPP9GyZct8yFi7ZDIZBgwYgDp16qBx48aIj48XbbNnzx6dnRFLhcPkyZOxd+9eyevMzc2zO8+ULVsWZcqUgaWlJczMzCQ/u86aNQuHDx/Wdco6p6goQRuv8VJjFMbuKZqS6hKor2IQqXm19X6u7v3t7++PuXPnysVOnjyJn3/+OfuyIAgICAiQ20aqiKRZs2b4448/si8HBQUhMjJSblk7qSVici4xIyW/u8cV9CLx/FCtWjUEBQVh7dq1WLJkSZ5Lw30UGRmJ5cuXY+XKlRgyZAgWLVqkcrdObctZuKQOqd9wFH3W4+NVPbzdPpB6r2AxCBGR7rEYhIiIqJBRVPBx9epVjBo1Kp+zEVN0RrfU2d+akGrrWlA7BeQ82+yjvIp3UlJSsGPHDlE8Pj4ejRo10kpuwIcferZs2YIxY8ZobUxleXh4SMavXbum87kVzZGfxSCKurJouy3033//XeCLQXr16oXx48fL/UC0bt06URv4MmXKFPiDrh4eHjh69Khc7O3bt3j+/HmhWTYjv0i9Z0gdbCf9c3d3x9atWxEbG4v9+/fj5MmTOH36NMLDw/Pc98mTJ2jdujV+/fVXTJo0KR+y1b4aNWrg119/xciRI0XXKXqfp8/D/fv3sXTpUlHc0dERM2fOxMCBA1U60FFQP8+qStHZ6gkJCQqLx5Ul9T2gqCxjoQqpJXciIiL0kIn0/S11P6lD3fu7UaNGMDU1lTuoHRgYiJSUlOwCk7t374oKeKWKQfz8/GBoaJh9gFUQBJw6dQo9evTI3kbqvUBqrJwK2rIjnwtjY2OMGjUKo0aNwuXLl3H48GEEBATgypUreRa9ZmZmYs2aNTh79iwCAgK0svyVurTxPJP67K3odx0+XtXD2+1DtxKpZWKUXT6ZiIjUx2ViiIiIChkPDw/JH7/OnDlTIFpIK/oBW5vtPVNTU5GWlqb03PqUlZUlWuIC+PBjQJMmTXLdd8+ePfnWFjW3pWL8/PwgCIJa/wYNGpTrvCVLlkTlypVF8cuXL+v07JnY2Fi5NcQ/cnFxybeD9c+fP8+3A4gHDhxQuL5zQWFra4suXbrIxXbu3CnqZDNw4ECN15/XtaZNm0rGc555SoCDg4Molt9nzmmT1A+cRY2dnR0GDhyIjRs34vnz53j69Ck2b96M4cOHw83NTeF+giDg+++/x759+/IvWS0bPHiw5BnAYWFhBeIz2OdOX8+/FStWiJaGKV68OK5du4avv/5a5TNei8pyJ4o+l2uj4E/q87HU+0lR5+rqKoq9fPky/xOB9P2tjftaEATJg93K3N/m5uZo2LChXCw1NRXnz5/Pvpzzs7iDgwNq164tGsvW1lZUyP/pvi9evBAtQVmuXDlUqlQpzzwVFU7dv39f7e9guf17+vRpnjl9burVq4dffvkFZ8+eRVxcHM6dO4c5c+agVatWuXa4efDgATp06KDXLgza+L1AagxFxSCKHq/Jyck6ebyePn1a47+vIJC63YoVK6aT20wQBKxfvz7//8g8KHp/cnFxyedMiIg+PwX7V1QiIiISMTY2RqtWrUTx0NDQAnFmqqIf5pRtvaqMkJAQlebWp6NHj0qeNd24ceM8i1dyK9DQths3biAoKCjf5vvUl19+KYq9f/8eW7Zs0dmcW7Zswfv370Xxjh076mzOnDZs2ICsrKx8mSstLQ2bN2/Ol7k0kXP5l5wH16S2KYjat28vGV+zZk0+Z1Lwfdpe/aPHjx/n2/xSZ+lJPe6UVdCLrnTBxcUFffv2xapVq/Dw4UOEhITg559/hrOzs2hbQRAwadIkjW5jfTIxMYG3t7conpmZme9rwRcFReX5d+DAAVHs999/lzxQr4zIyEgNMyoYFH3ODQ0N1XjsJ0+eKD1fUSb1GHvx4kX+JwLp2//169eSn7dVERoaKllsp+z9LbVMy6ffmXN+f27atKnCouOcY+U2jqK5pZQtW1Yy/jl+pigITE1N0bhxY0yZMgVHjx5FVFQU/vnnH8nfYIAP3SY3btyYz1n+n0ePHmk8Rs5CJuBDdyspfLyqR+p2+9w+O0oVgzg6Oup9qSUios8Bi0GIiIgKof79+0vGV65cmc+ZiFWoUAEWFhai+N27d7U2h6KxatSoobU5tEEQBMyYMUPyurw6Zjx9+jTfuwj8/fff+TrfR/369ZOMr127Vmdz/vXXX5Lx/CoG0cfZOvlZXKQuf3//XM8MatKkCSpWrJiPGamnSpUqkstAXbhwQauvhUWB1Nm3ERERkgf6dMHa2loU02RZM32dkV2QVK5cGbNmzcKjR48kC6OePHmCixcv6iEz7ShevLhkvKCuzV6QFYXnX2RkJJ49eyYXs7KyQufOndUaLz09HXfu3NFGanpnaWkp2W0tZ8cvVUVGRkoWPFStWlWjcQsjqe8++VlQ+Smp2z8jI0Pjx7PU48XU1FTpz4NSy7R8LNzIzMzE2bNn5a5r3ry50mM9efIk+/l/6tQppeaWYm1tjTJlyojiOV9bSD/Mzc3RuXNnHD16FAcOHJD8rWPTpk16yOyDoKAgjbqTZWVlST5PpT6jA4Cbm5tkMScfr7lT9Br5OX13kCo6qlmzph4yISL6/LAYhIiIqBBq06aN5I+r+/fv1/gHVk0ZGRmhXr16ovi5c+e0NseFCxdEMTMzM3h4eGhtDm1Yvnw5rl69KooXL14cvXr1ynXf9evXi37UsbOzw/v377XSNnThwoWiObds2aKXFut16tSBl5eXKH7r1i3s2LFD6/NJLT0CfDiAr2h5D207c+aM5Jmxly5d0sr9e+3aNdHYt2/f1vvrQ15kMlmuhVKFoSvIRyNHjpSMKyoQ+1x5eHhIHhA+ceJEvswvtezamzdv1B5P6v0pv8hkMr3NLcXW1hbbtm1DiRIlRNd92qK/sJFa9sDQ0FCyyw3lrig8/96+fSuKlS9fHqampmqNd/36daSkpKidT0F7HWjQoIEodubMGY3GlCqWNjIykvwsWdR5eHjA0NBQLhYVFYVXr17ley7ly5eXLJbTxf3t4eEBExMTpfb38vISfc64ceMGYmJicPXqVdFrem4FHI0aNRI9tz8WlmjSGQSQfq5wecGCp127dpg5c6YofvHiRb0tF5eYmIhLly6pvf/ly5eRlJQkFzMxMVFYDGJmZoY6deqI4vp6vOrqfU/b41asWFGya97n9Dy/ffu2KPY5vncTEekDi0GIiIgKIUNDQ0ydOlUUz8jIwIABA5CamqqzuZVp/9moUSNRLDg4WCvLkGRkZGDXrl2iuJeXF4yNjTUeX1tOnz6NSZMmSV43c+bMXA8SKOoa0aVLF7UPLuTUs2dPUQvkyMhI/Pvvv1oZX1VSj2cAGDduHGJiYrQ2T2xsLMaNGyd53ffff59vB1GkurBUrFhRspBKHZ6envjiiy+UmregGThwoOT9YGVlhe7du+shI/UMHDgQ5cuXF8X37Nmj0yWQMjMzERsbq7Pxtc3Q0BCNGzcWxVesWJEv85cqVUoUu3v3rtpLOOnrNRSA5PuDPgr8PmVpaYl27dqJ4poc8Nc3qWXvnJycFC4rQIpJPf/U/awoCAIOHjyoaUoqi4uLE8U0aXeuqHOZsgra60DDhg1FsWPHjiEiIkLtMaWWY6hZs6bk2fpFnYWFheTZ5vpa+lHq/tZkmcK0tDTJwnCpwglFjIyM0KRJE7lYVlYWTp8+LSrgKFu2LNzc3BSOZW5uLvobT548iQcPHojO7nd3d5d8jVNE6r3y8OHDOv1eT+qROqkjNTVVq99ZVaXJdwupriYeHh65/u4g9Xjdu3ev2jloQlfve7oYV+p2++effzQaszCRem+qW7euHjIhIvr88NcKIiKiQmrw4MGSLRXv3r2L7777TidzHjx4MM/lTQAoPGC7bNkyjXPYvn275FrqPXr00Hhsbfn333/Rrl07yR/vGjRogK+++irX/U+ePCnZZrVPnz5ay7FMmTLw8fERxfW1lEj79u3h6+srir99+xYjR47U2plWX3/9teRByEqVKqFv375amSMv8fHx2LNnjyjeu3dvrc4jNd7WrVsL/I/K5cuXx7Fjx7B37165f0ePHoWlpaW+01OasbExfv31V8nrxowZo5NlUBITE9GpUyfcunVL62PrktT7SlBQEPbv36/zud3c3ERnDCclJam1jMnt27clzwzOL1IdVnKe6akPUh0zCuuSKjdv3pRcgkHqACjlTaqjW0hICMLDw1Ue699//8WjR4+0kZZKpLqbqNuV4dWrVxoXCxa014FOnTqJOldkZGSo/Z0gODgYR48eFcULU7Gotkl1tbty5YoeMgG6desmit2+fVvtM983bNggeSKCqve3oqVicr5nK7OsS85tTp06Jfner+wSMR916tRJVEj2+vVrrF69WqVxSPcUdQLT52ebjRs34vXr1yrv9/r1a8liEEXLEn/Ut29fURHsjRs3cODAAZVz0JSu3vd0Ma7U7bpv3z69FfDlp7S0NNHfKZPJJH8DIiIi7WMxCBERUSFlaGiIjRs3SnbD+OOPPzB58mStHUBPS0vD999/jw4dOiAhISHP7WvWrCm53vLatWvVOsD2UWxsrGS3DXt7+wKxfMS7d+8wYsQIdOrUSfKHAicnJ+zYsSPPs4elCjJKliyp9SVMpIpLjh49qtYPSdqwdu1amJubi+I7d+7Et99+q/HjeeLEidi2bZsobmBggHXr1uVbZ5kdO3YgOTlZFNdmsY+i8aKjo/PlALumWrRogU6dOsn9k+o4VNB169ZNslAtNjYW/v7+kh0G1HXt2jV4eHjo5cx4TXXt2hUVK1YUxYcPH67R2ePKkMlkkgek165dq9I4aWlpGDp0qLbSUou9vb0o9vTp0/xPJAepwqfSpUvrdM5r165h0KBBWi0OyMrKUthZqmPHjlqb53Pi5OQEFxcXuZggCCp3x4iJicE333yjzdSUVrJkSVHs2bNnCA4OVmkcQRAwZMgQjZaIAQre60C5cuUknx+//vorwsLCVB5v9OjRyMjIkIuZmZlh2LBhaudY2LVp00YUO336dP4ngg9FGlJLg33zzTei+y0vUVFR+PHHH0VxLy8v1K9fX6WxpJZrOXLkCAIDA+Vi6hSDvHnzBsuXL1dqztzY2NhIPo6nTZum8usJ6ZbU5xoTExO9LheXkJCgsCtpbiZOnIjExES5mKWlJfr165frfhUrVpR8bR8zZky+d3+ztLQULRsVFxencadEqfdTqRN2VNG0aVPR9w5BEDBo0KACUcCtS5cuXRJ9xqlbty6KFSump4yIiD4vLAYhIiIqxGrVqiX54xMAzJ8/H+3btxe1rFXV4cOHUaNGDSxYsEClg/FS3UkEQUDnzp1x48YNlfOIiopCq1atJNdmHzVqlN46BmRmZuLixYsYNWoUypcvj9WrV0veTg4ODjh+/DjKli2b63hxcXGSLVallnXRVLdu3UQFEJmZmZLtt/NDpUqVFJ79tnTpUnTr1k2tH3Xi4+PRu3dvLFq0SPL6CRMmSC5ToStSS7XUrl0bVapU0eo8X3zxBTw9PUVxfXV/+VytXr1asoX78+fP4e3tLXk2nioiIyMxZswY1K9fXy9nxWuDoaEhpkyZIoq/e/cOLVq0ULtALSMjQ6liEqkzmTdu3IizZ88qNU96ejoGDx6M69evq5yjNkk9zu7fv4/4+Hi1xlu9ejU2b96s8gG8Tz158kTyLFFdt4TOyMjAhg0bUKVKFfTv31/j+yYtLQ39+vXDuXPnRNc5OjqyGEQDUs+/BQsW4OHDh0rtHx8fj65du+L58+faTk0pDg4OqFatmij+008/KT2GIAj49ttvcezYMY3zkXoduHz5stYKxNXx7bffimLv379Hx44dVVpWYeLEiZIdJgYMGABHR0dNUizU/Pz8RMXUly5d0ksnOGNjY4wePVoUv3v3LgYPHqz04zA5ORmdOnWS7Aoyfvx4lfOqWbOm6EB9aGgo3r9/LxdTpoDDy8sLNjY2crH79+/LXTYwMFCriP/nn38WPZZjY2PRtm1brRSEPHr0SG/f8wqChIQEfP3115IdvlTx+++/i2Kenp75ttyoIlu3bsXs2bOV3n7mzJmSJ0oMHz5c9BiXMn/+fNFSKs+fP8eXX36p8W9QwIdubMouoSL1PTpnsZeqSpUqBTs7O7lYbGysxs/FRYsWiR4rN2/eRJcuXbSy1OeZM2fw33//aTyOtkm9f0sVMxIRkW6wGISIiKiQGzZsGKZOnSp53aFDh+Du7o7vvvsOoaGhSo8ZHx+P9evXw9PTE19++aXSP8h/qmXLlpJnN7179w6+vr6YPXu26CwUKVlZWdiyZQu8vLwkWx7XqlVL4d+vqhcvXuDSpUuS/y5evIhTp05h3759WLlyJX744Qe0bdsWTk5OaNSoEVauXCnZ7QH4cFD+7NmzqFOnTp45bNu2TfKsUG13jQA+HMBo3bq1KL5+/Xqtz6Wsfv36Yfr06ZLX/fPPP6hSpQqWL1+u1JkzKSkpWLNmDapWrYrt27dLbtOlSxfMmzdPo5xVERISgkuXLoniurh/FY17/PhxrfxAR8qxtbXFoUOHUK5cOdF18fHxGDBgAOrXr49//vkHaWlpSo97/fp1jBkzBi4uLli+fHmhXXbjoyFDhqBz586i+O3bt7NvH2XFxsZi+fLlqFSpEg4dOpTn9n379oWZmZlcTBAEdOjQIc+Ds7du3YK/vz+2bt0KALCwsFA6T22zs7NDhQoV5GLp6emYO3euWuPdv38f/fv3R4UKFTBz5kyEhISotP+dO3fQpk0b0cG24sWLq9w+X12ZmZnYvHkz6tati2rVqmH+/PkqfR7KzMzE/v37UatWLckDJgAwb9480cECUp5UR53k5GQ0a9YM165dy3XfM2fOoFGjRtkHGPT1/OvUqZMotnfvXowdOxbp6em57vvmzRv07NkTS5cuzY7lXFZFFdWqVRMdnHvz5g1WrVql9pia8vHxkfxOcOfOHTRt2hR37tzJdf+EhAQMHz5csqi3dOnS+fo5riAyMzPDl19+KRdLSUlRuqBR27777jvUqFFDFN+8eTN69uwpudznp0JDQ9GyZUucP39edF3btm3VWlZRJpPlWehRpUoVlCpVKs+xDA0N81zWoE6dOpJdBfLi4OAg2Zns6dOnqFu3Ln7//XeF3zcVSUxMxO7du9G+fXtUrlw5+/PK5ygzMxMrVqxA5cqV0blzZ/zzzz8qdWNKT0/H1KlTsWbNGtF1+bXcqJRP3/umTp2Kr776CnFxcQq3j4uLw9ChQyW/c7u4uGDmzJlKzevm5ob58+eL4jdu3ECtWrWwYcOGPN8Dc4qOjsbGjRvh6+sLDw8PHD9+XKn9pE6AmD9/vsZFcVLdA2fPno2srCy1x/T19ZXsNHf8+HHUrl0b//77r8oFnK9evcLKlSvh4eEBPz+/PD8/6YPUd6quXbvqIRMios+Tkb4TICIiIs3NnDkTlpaW+PHHH0VfHBMTE7Fw4UIsXLgQtWvXRuPGjVG1alWUK1cO1tbWMDQ0RFJSEl69eoUHDx4gMDBQa2eTLV26FNeuXcPNmzdFOU2dOhULFiyAr68v/Pz8ULZsWTg4OMDY2BjR0dF4+/YtLl68iJMnTyo8cG1jY4Pdu3eLDuKp66+//lK5NXluDA0NMWLECMybN09yzVkpUl0j3Nzc4OXlpbW8PtWnTx/RWdshISG4ePEiGjZsqJM58zJjxgzIZDLMmDFDdN2bN28wZswY/Pjjj2jRogUaNmwINzc32NnZQSaTIS4uDo8fP0ZgYCCOHTuW6w9hrVq1wrZt2zQ66KIqqftXJpOp9cO2Mnr16oXvvvtO7gerrKwsbNiwQbITA+mGq6srzp07h5YtW0ouDXP58mV07doVtra28PPzg5eXFypUqIBixYrB3NwcqampiIuLw5MnTxAUFIQzZ85o3Ka4IFq3bh1u374tOlj//PlzdO3aFXXq1EGXLl3QvHlzlC1bFk5OTsjMzERMTAyePHmCa9euISAgAMePH1epsMbe3h7ff/+96MfvuLg4tG7dGv7+/ujYsSPc3NxgZWWFyMhIPHr0CEePHsXp06fl3neXLVuGIUOGaHZDaKBbt2749ddf5WLz5s1DYGAgOnfujC+++AI2NjaSr3uK2u6Hh4dj+vTpmD59OqpXrw5fX194enqiVq1aKFasGOzt7WFmZobExESEh4fj1q1b2LdvH/bt2ydZpPTrr7/m6+vuR/fv38fkyZMxefJklChRAg0bNoSXlxdKlCgBR0dH2NvbIzU1FfHx8Xjy5Alu376NY8eO5dpdpnPnznpfHqiwq1KlCgYMGCA6W/3FixeoV68e2rdvj7Zt28LV1RWmpqaIiIjA/fv3cejQIbkiYQMDAyxduhRfffVVfv8J+Pbbb7F06VLRUorLli3Df//9h6+//hr+/v5wdXWFsbEx3r59i+DgYOzfvx+bNm2S269y5cqoVasWdu7cqVYuxsbG6Nixo2j/UaNG4fDhw2jTpg0qVKgAa2trUcc5U1NTpQqX1bF48WKcPn1a1MHq9u3b8PT0RK9evdCzZ0/UqFEDxYsXR0JCAp4+fYp///0X69atw4sXL0RjymQybNiwQa2D7kXNgAEDsHv3brnY7t270aJFi3zPxdTUNLuQP+f3yV27diEgIAADBw5Ely5dUKFCBTg4OCAiIgIhISHYtWsXNm3aJFnw4OzsLPk5Wln+/v65Pq9UKVL09/eX7Hr16fXq6tSpE2bNmiU62SE5ORnjx4/HzJkz0atXL/j4+KBOnTpwcnKCnZ1d9vtXdHQ0goODERQUhKtXryIgIEAvXWIKsqysrOzPKZaWlmjRogW8vLzg4eGBSpUqwd7eHra2tkhPT0dMTAwePnyIgIAAbNy4UXLZrSpVquj1s8DIkSOxa9cuhIeHA/jwm8bu3bvRuXNn+Pn5ZRc5vXr1CgEBAdi3b5/kd2QDAwOsXr0aVlZWSs89btw43L17V1TEFBUVhUGDBmHKlCno2bMnGjdujJo1a8LBwQG2trZISUlBXFwcIiMjce/ePdy5cweBgYE4f/68WgXu3bp1E70+nDlzBjVq1EC/fv2y5865nAzwoaOWok4o3bp1w6lTp+RiW7duRXBwMHr16oWqVavC1tZWcrnZOnXqiIozP1qwYAFCQkJw9OhRufizZ8/QsWNHVKpUCd27d0ejRo1QtWpVODg4wMrKCklJSYiLi8O7d+9w9+5dBAUF4fz587h69apeO4Dl5dWrV6ITYmrXro2aNWvqKSMios+QQEREREXG4cOHBWdnZwGATv7Z2NgIf/75p0o5vXv3TmjatKnWc3FxcRGuX7+u9m2lq9sIgGBkZCT06dNHCAoKUimnu3fvSo43bdo0tf/OvCQlJQlWVlaiOb/66iudzams7du3S+amjX+TJk0S0tPT8/XvSU9PF0qUKCHKpUmTJjqdV+r55+bmlus+UrfZ9OnTlZ5z+vTpov0bNWqk4V+iPBcXF43y15X4+Hihd+/eOn398fPzE16+fJlrHlL3j7K3T0BAgGhfX19fzW+c/+/JkyeCq6ur1m6PdevWKTVvamqqUKtWLY3m+uGHHwRBkH7+KMvX11e0b0BAgEq3n5mZmVr55zRu3DitPz4HDhyo9N+iicDAQJ0+zwAI3bt3V+l9pCA97wYOHKj2c0WKJo95QRCE6OhooXTp0hrdHytWrBDCwsJEcRcXF6XzkHrvCAsLU2rftWvXavyYsre3F+7evavx/XP+/HlBJpOpPH9ut5Umj9+PQkJCJD8Hqftv2bJlKs2/bt06rb8mafrY15b09HTRd8BixYoJmZmZao2n6XuRIAjC7t27BSMjI63c19bW1kJgYKBaf8tHjx49ynWOvXv3Kj1WUFBQrmMdPXpUo1wFQRDmzJmjtefKp/9atWqV59yavpbmB3WezzExMVq/Pe3s7IQbN27kzx8tKH4tvnLlimBubq7R37JkyRK1csrMzBRGjRqlk8friBEjlM7B3d1drTlye22Li4sTnJyc1Bo3r88PycnJQseOHXVyu82dOzfP20wX74mK/PHHH6K5Fi1apJO5iIhIGpeJISIiKkLatGmDkJAQfP3115JnJ6jL1NQU48aNw5MnTzBq1CiV9nV2dsbx48cxceJEGBlppylZ69atce3aNcm2nfpiamoKX19fLFmyBM+fP8eWLVskWyTnRtHZbrpaQgT40Fa2Y8eOovjOnTtVbkOsbT179sT9+/cl26+rq3z58vj333+xYMECrT0elXXkyBG8efNGFNfl/ato/EePHkm23ybdsra2xtatW3Ho0CFUrlxZq2PXqFEDhw4dQkBAgFJtzguqChUq4MqVK2jVqlW+zmtiYoITJ06odVa8TCbDrFmzCsRSBRUqVJBcy17fZDIZJkyYgHXr1uXLfMWLF4e3t7doTXZtcHR0xMqVK7F9+/Z8fx8pquzt7XH69Gm4uLiovK+JiQn+/vtvjBw5UgeZKW/o0KH4+eef1d6/RIkSOHbsGKpVq6ZxLo0aNcIPP/yg8TjaVrlyZVy8eBG1atXSaBwLCwts27YNo0eP1lJmhZ+RkZGoK9W7d+9w8uRJPWX0of3/4cOH4ejoqNE45cuXx7lz5xR2r1JWpUqVJJfsAz50RPDz81N6rOrVq6NYsWKS15mYmMDHx0edFOVMmTIFBw8eRPHixTUe61Pa/I3gc1euXDmcO3dOZx2VVOHl5YUjR46otWydqakp1q5di2+++UatuQ0MDPDnn3/i77//VrobqrKUfbwaGBhg69atMDc31+r8NjY22LBhg0462pmbm+Off/7B3LlzJTuWaKKgPc9zLrVobm6O/v376ykbIqLPE4tBiIiIihgHBwcsX74coaGhmDx5ssIfvZTh7e2NZcuW4eXLl/j999/h5OSk1jhGRkZYuHAhHj9+jNGjR6v1JV0mk6F9+/a4ePEijhw5onYu6pDJZDA1NYWNjQ3KlCmDOnXqoHXr1hg9ejT++OMPnD17FnFxcTh9+jS++eYblCxZUuU50tPTsXnzZlHcw8ND6weNc5IqFoiPjxe1m9aHsmXLYu/evbh+/Tr69u0rtyayKqysrPD7778jJCQE7du313KWypEq9jE2Nkb37t11Om+3bt0kf2DSpNU2aaZt27a4f/8+/vnnH7Ru3VrtH+zs7OwwbNgwnDt3DkFBQWjbtq2WM9UPZ2dnHD16FFu3blX79c/CwgKDBw9W6eCOs7MzTp8+jQkTJij9o2zNmjVx+vRpjQ4Ca9uIESOwb98+lC5dWqNx+vTpgyFDhqBEiRIajePt7Y3z58/jt99+00lxhpTy5cvj8uXLePnyJVauXImOHTtq/LmhWrVqmDNnDh4+fIgRI0aIltggzVSqVAmXLl3CoEGDlL5tfXx8cO3aNQwePFjH2Sln1qxZ2LZtm8oHv7t27Yrr169rdUnAuXPnYtWqVXBwcNDamNpQvnx5XLlyBbNmzVL5oKVMJkPnzp1x9+5d9OrVSzcJFmJjx44VfZ5YvXq1nrL5oEWLFrh37x4GDRqkcvGchYUFJk2ahKCgII0LiD5StHyLp6enSo9HmUymcKx69eqp/X0lpy+//BIPHz7ETz/9pNFz2djYGG3atMH27duxa9cureRWGFlZWWHevHlo3LixRgf3LS0t8dNPPyE4OBjVq1fXYoaa8fX1xe3bt9GxY0elP2/5+vriypUrWlnmZvDgwXj06BHGjBkDS0tLtccxNzdH9+7dceDAASxevFjp/erUqYNr167B29tb7bmltG3bFmfOnNHJbzIGBgaYPHkygoOD0a9fP42KQmxtbTF48GAEBARgwoQJWsxSM/fu3cPFixflYv3798/X3/OIiAiQCUIBXlCMiIiItOLGjRvZa4k+efIEz58/R1xcHFJSUmBiYgJ7e3vY29ujRIkS8PDwgJeXF+rVq6dRIUlukpOTERgYiHPnziEwMBBv3rxBdHQ0oqOjkZGRAXt7ezg4OMDJyQl16tRBkyZN4OPjo/AMrKLgxYsXorV2gQ9nd+p6ve+MjAz873//Q1ZWlly8Ro0a6Nq1q07nVlVSUhJOnjyJ8+fP4/bt2wgLC8O7d++QlJSEjIwMhfsZGBhg27Zt6NGjRz5m+38EQcDcuXORlpYmFy9dujSGDRum8/n/+uuv7HWkP7K2tsbEiRN1PjflLSYmBgEBAbh06RLu3r2Lp0+f4u3bt9mPa1tbW9jZ2cHBwQGVK1dG3bp14eXlhbp16ypci7qoEAQBJ0+exJ49e3D27FmEhISIXqsAwMzMDG5ubqhXrx5atWqFli1bKlz/Wxnh4eHYu3cvjh49iocPHyIiIgLJycmwtrZGhQoVUK9ePXTp0gXNmjXT5M/TqczMTBw7dgwnTpzArVu3EBoaivj4eCQmJkq+Xir6aUAQBNy+fRsXL15EYGAggoKCEBoaisTERMntbW1tUbNmTTRq1Ai9e/cuUOuBBwcH49KlSwgJCcHDhw/x5MkTREdHIyEhAUlJSTAzM4O1tTVsbGxQokQJ1KhRAzVr1kSDBg1U7vZF6nvw4AH27duH48ePIywsDBEREUhNTYWtrS3c3NzQqFEjdO/eXesHfLQlKSkJa9aswb59+3Dp0iWkpqbKXW9oaAh3d3e0bNkSQ4YMER1MPHnyJIKDg+VizZs3h7u7u8q5pKam4t9//8Xp06dx+/ZtPH36NPvxnpmZKbeti4sLnj59qvIc6kpISMCOHTuwf/9+XLx4EdHR0aJtjI2NUbt2bbRq1Qr9+vXTeYF0YdevXz9s2bIl+7KxsTHCw8O13l1CHR87Jx4+fBjXr19HSkqKaBtra2vUr18f7dq1Q58+fbR+sPDKlSs4fPiwKF63bl20a9dOpbEuXryI48ePi+L169dH69at1c5RkZSUFBw6dAgHDx7EpUuX8OjRI8nPQwBQqlQpuLu7w8PDA/7+/mjSpIlGB+eLoujoaJw/fx6BgYG4cuUKHj58iJcvX0p+FjIwMEDFihVRp04dtG/fHp07dy7wt2dwcDB27tyZ/dn54+8stra2qFSpEho3boyePXtqtQjxU3Fxcdi/fz8OHz6MK1eu4OnTp5K3rUwmQ7ly5eDu7o66deuiWbNmaNiwocbfb27cuIG9e/fi1q1bCA4ORmxsLBISEkTfxQEgICBA6eLxs2fP4tChQ7h16xYePnyI+Ph4JCQkID09XbRtWFgYXF1dVcr73bt3+Oeff3D06FFcu3YNL1++lNzO0NAQ5cuXR5UqVVCvXj00a9YMXl5eOulgoqlx48Zh6dKl2ZdlMhnu37+v1mcaIiJSH4tBiIiIiKhIOXnyJNq2bSv6scfExASHDh1C8+bN9ZQZEWkqPT0dL168QFxcHDIyMmBpaQkbGxuULFmSnRryWURERPaP68CHVtq2trZwdnbWc2ZEBUdaWhrevn2LqKgoCIIAGxsblC1bVust4YuCyMhIvHnzBikpKTA2Noa9vT3KlClTIA9uFVR37txBrVq15A66zpo1q0B1rwI+FBm+fPkSUVFRSEtLg6mpKYoXL14gilYKi/T0dLx8+RJxcXFIS0uDhYUFrK2t4ejoWOALFQqq1NRUvH37FgkJCUhOToaFhQVsbGzg5OSk9eVHPjepqal48eIFEhISsj+/W1tbw8nJCWZmZvpOr8BKTk7Gy5cvkZiYiMzMTFhZWWU/JgvD54jExESUK1cOMTEx2bHOnTvjn3/+0WNWRESfJxaDEBEREVGRs3XrVvTr1090BpKVlRVOnTqls7OgiIiIiIj0pU+fPti2bVv2ZWdnZzx79owHs4mIKF/99ttvmDRpUvZlAwMDBAUFoVq1anrMiojo88RTp4iIiIioyOnTpw8WLFggiicmJqJt27Z48OCBHrIiIiIiItKdX375BUZGRtmXIyIi8Ndff+kxIyIi+tykpaVh0aJFcrE+ffqwEISISE9YDEJERERERdLEiRMxfvx4UTwyMhItW7bEixcv9JAVEREREZFuuLm5YdiwYXKxBQsWiJZPJCIi0pV169bh1atX2ZfNzMwwc+ZMPWZERPR5YzEIERERERVZv/32G3r16iWKP3/+HK1atUJ0dLQesiIiIiIi0o3Zs2fD0dEx+/Lz58+xfPlyPWZERESfi6SkJPzyyy9yse+//x7ly5fXU0ZERMRiECIiIiIqsmQyGTZs2AB/f3/Rdffv38eXX36J5ORkPWRGRERERKR9Dg4OmDt3rlxszpw5iIuL01NGRET0uVi0aBFev36dfdnV1RWTJ0/WY0ZERCQTBEHQdxJERERERLoUHx+P4cOHIzY2VnRdmzZtMG7cuPxPioiIiIhIB7KysrBgwQKkpKRkxzp06AAPDw89ZkVEREXdokWLEB8fn325RYsWaNSokR4zIiIiFoMQERERERERERERERERERERFSFcJoaIiIiIiIiIiIiIiIiIiIioCGExCBEREREREREREREREREREVERwmIQIiIiIiIiIiIiIiIiIiIioiKExSBERERERERERERERERERERERQiLQYiIiIiIiIiIiIiIiIiIiIiKECN9J0CkyPv373Hnzh0AgLOzM4yM+HAlIiIiIiIiIiIiIiIiIqKiJSMjAxEREQCAGjVqwMzMTOMxeXSdCqw7d+7A29tb32kQERERERERERERERERERHliytXrsDLy0vjcbhMDBEREREREREREREREREREVERws4gVGA5Oztn///KlSsoWbKkHrMhIiIiIiIiIiIiIiIiIiLSvtevX2evmvHpcXJNsBiECiwjo/97eJYsWRJlypTRYzZERERERERERERERERERES69elxck1wmRgiIiIiIiIiIiIiIiIiIiKiIoTFIERERERERERERERERERERERFCItBiIiIiIiIiIiIiIiIiIiIiIoQFoMQERERERERERERERERERERFSEsBiEiIiIiIiIiIiIiIiIiIiIqQlgMQkRERERERERERERERERERFSEsBiEiIiIiIiIiIiIiIiIiIiIqAgx0ncCRVlUVBQePnyI8PBwvH37FklJScjKyoKtrS2cnJxQq1YtVK5cGTKZTN+pAgAiIiIQGBiI0NBQJCYmwsLCAi4uLvD29kbZsmX1nR4REREREREREREREREREREpgcUgWnT79m0cOnQIFy5cwM2bN/H69es897Gzs0OvXr0watQo1KxZMx+yFDt79ixmz56NkydPIisrS3Kb+vXrY/LkyejYsWM+Z0dERERERERERERERERERESqkAmCIOg7iaKiX79+2LJli1r7GhgYYMyYMZg3bx7Mzc21nJm0jIwMTJgwAX/88YfS+/To0QN///03LC0tdZjZBy9evMjuSBIeHo4yZcrofE4iIiIiIiIiIiIiIiIiIqL8pItj4wYaj0BKMTExgaOjI6ysrCSXhcnKysLSpUvRpk0bJCYm6jyfrKws9O3bV2EhiK2trWR8586daNu2Ld6/f6/L9IiIiIiIiIiIiIiIiIiIiEhNLAbRgRIlSqBXr15YsWIFAgMDER0djdTUVERGRiIhIQGJiYm4cOECxo0bJ+oCcubMGYwYMULnOc6dOxc7d+6Ui9WoUQM7d+5EQkICYmNjkZycjMOHD6NRo0Zy2509exbffPONznMkIiIiIiIiIiIiIiIiIiIi1XGZGC3at28fnJ2d0bBhQ8nuH1KePHmC1q1b4/Hjx3Lxs2fPwsfHRxdpIjw8HG5ubkhNTc2OtWzZEnv37oWFhYVo+4yMDAwdOhQbN26Ui1+5cgVeXl46yRHgMjFERERERERERERERERERFT0cZmYAq5Tp05o1KiR0oUgAFCxYkUcPHgQJiYmcvFNmzZpO71ss2bNkisEKVmyJHbs2CFZCAIARkZGWLt2LapXry4X//nnn3WWIxEREREREREREREREREREamHxSAFQOXKldGhQwe52JkzZ3QyV0REBNatWycXmz17Nuzs7HLdz9jYGL///rtc7Pjx47h165Z2EyQiIiIiIiIiIiIiIiIiIiKNsBikgKhfv77c5VevXulkngMHDiAjIyP7sq2tLXr16qXUvv7+/qhUqZJcbO/evVrNj4iIiIiIiIiIiIiIiIiIiDTDYpACwtraWu5yVlaWTubZv3+/3OV27dopXB4mJ5lMhh49euQ6HhEREREREREREREREREREekXi0EKiJcvX8pdLlu2rE7mCQgIkLvcqFEjlfZv2LCh3OXbt28jKipK47yIiIiIiIiIiIiIiIiIiIhIO1gMUkAcPHhQ7rK/v7/W5wgPD0dCQoJcrF69eiqNkXM5GwAIDg7WKC8iIiIiIiIiIiIiIiIiIiLSHhaDFAArVqzAjRs3si8bGhpizJgxWp8nJCREFKtQoYJKYzg6OsLGxibPcYmIiIiIiIiIiIiIiIiIiEg/WAyiR4mJiZg6daqo8GP69OmoWrWq1ud7+PCh3GVra2vY2dmpPE7OJWwePHigSVpERERERERERERERERERESkRUb6TqAoEwQBq1atkoulpqYiKioKQUFB+O+//5CUlJR9nYGBAX766SdMnTpVJ/lER0fLXS5RooRa45QsWRL37t3LvhwTE6NRXkRERERERERERERERAWNIAh4//494uLikJqaiszMTGRmZuo7LSIi0jJDQ0MYGhrC1NQUtra2MDMzg0wm03daGmMxiA5lZmZi1KhReW5nZGSENm3a4Oeff4a3t7fO8klMTJS7bGFhodY45ubmuY5LRERERERERERERERUWGVkZCA2NhZxcXFIS0vTdzpERKRjGRkZAIDk5GTExMTAxMQEtra2sLOzg5FR4S2pKLyZFyGNGzdG165dUatWLZ3O82kXEgAwMzNTa5ycxSA5x1XWixcvcr3+9evXao1LRERERERERERERESkjvT0dDx79gzp6emi62QyGQwNDfWQFRER6VJmZiYEQci+nJaWhoiICMTGxsLFxQXGxsZ6zE59LAYpAE6fPo3Tp0/jxx9/xJ9//olOnTrpZJ6UlBS5yyYmJmqNY2pqmuu4yipbtqxa+xEREREREREREREREWlbZmYmwsPD5QpBLCwsYGtrC2traxaCEBEVYZmZmUhISEBcXBySk5MBfCgQDA8Ph4uLS6F8DzDQdwJFmZGREQRBkPuXkJCAJ0+eYNeuXejdu7dcQcbr16/RuXNnLFiwQCf55OwEom5rs9TU1FzHJSIiIiIiIiIiIiIiKkyysrIQHh6efQzE2NgYFStWhIuLC+zs7ArlQUAiIlKeoaEh7Ozs4OLigooVK2Z3A0lNTUV4eDiysrL0nKHq2Bkkn1lZWcHKygoVKlRAt27dEBISgt69e+PWrVvZ23z//fdwd3dH+/bttT73p96/f6/WODk7geQcV1nh4eG5Xv/69Wt4e3urNTYREREREREREREREZGyYmJiso9/GBoaoly5cmp3WCciosLNxMQE5cqVw9OnT5GZmYmUlBTExMTA0dFR36mphMUgeubu7o5Tp06hQYMGePDgQXZ87NixaNu2rVYrTXMWbXxsb6MqbRWDlClTRq39iIiIiIiIiIiIiIiItCkhISH7/2XKlGEhCBHRZ87ExARlypTBs2fPAACJiYmFrhiEy8QUAPb29vjjjz/kYs+ePcPhw4e1Ps+n3r59q9Y4r1+/znVcIiIiIiIiIiIiIiKiwiIjIyP7RFgTExNYWFjoOSMiIioILCwssosDk5OTkZmZqeeMVMNikAKiefPmKFWqlFwsICBAq3N88cUXcpfj4+MRGxur8jg5l3fJOS4REREREREREREREVFhkZSUlP1/a2trPWZCREQFzafvC4mJiXrMRHUsBikgZDIZateuLRcLCwvT6hzu7u6iWGhoqEpjREdHIz4+Ps9xiYiIiIiIiIiIiIiICoNPD+5ZWVnpMRMiIipoPn1fYDEIqc3W1lbucnJyslbHL1u2rOhDzOXLl1Ua49KlS6JYlSpVNMqLiIiIiIiIiIiIiIhIX9LT07P/b25ursdMiIiooPn0feHT94vCgMUgBUhUVJTcZWdnZ62OL5PJ0LRpU7nYhQsXVBoj5/Y1a9aEk5OTxrkRERERERERERERERHpQ1ZWFgDAwMAAMplMz9kQEVFBIpPJst8bPr5fFBYsBikgsrKycOPGDblYqVKltD5Px44d5S4fPHhQpQ4kO3fuzHU8IiIiIiIiIiIiIiKiwiQzMxPAh2IQIiKinAwNDQH83/tFYcF3tQLi4MGDiIyMlIs1b95c6/O0b98eRkZG2Zfj4uKwfft2pfY9deoUHj9+LBfr1KmTNtMjIiIiIiIiIiIiIiIiIiIiDbEYREtSU1PV3jciIgLjx4+Xizk4OMDPzy/X/VxdXbPb0shksjy3B4BixYph4MCBcrGff/4ZsbGxue6Xnp6Ob7/9Vi7WvHlzeHh45DknERERERERERERERERERER5R8Wg2jJ2LFjMXr0aDx//lyl/W7dugU/Pz+EhobKxWfOnAkTExNtppht2rRpcmO/fv0avXr1UrhcTEZGBoYNG4Y7d+7IxWfPnq2T/IiIiIiIiIiIiIiIiIiIiEh9RnlvQspIS0vDmjVrsGLFCjRq1AgdO3aEp6cnatasCUdHx+ztBEHA06dPcfXqVezYsQP79+8XrS3k7++PkSNH6izXcuXK4aeffsL06dOzY8eOHUP9+vUxbdo0tGnTBpaWlkhJScHZs2cxa9YsXLhwQW6MIUOGoF69ejrLkYiIiIiIiIiIiIiIiHRnxaqjWLH6qNbHHTW8NUaNaK31cYmISDUsBtEyQRBw/vx5nD9/PjtmaGgIGxsbZGVlISEhAVlZWQr3b9q0KQ4cOABDQ0Od5vnzzz/jzp072L17d3bszp076N69OwDA1tYW8fHxEARBtG/jxo2xbNkyneZHREREREREREREREREupOQmILXb2J0Mi4REekfi0HyQWZmJmJicn8ztbCwwC+//ILx48frvBAEAAwMDLB161YUK1YMf/75p+j6uLg4yf26du2K9evXw9zcXNcpEhERERERERERERERkY5YW5mjZAl7hddnZQl4+y5WLla8mB0MDGR5jktERPrHYhAtWbx4MVq3bo2jR4/iwoULePz4cZ77GBoaonbt2ujXrx/69esHJyenfMj0/xgbG2P58uXo3r07Zs+ejVOnTkl2AgEAb29vTJ48GZ07d87XHImIiIiIiIiIiIiIiEj7Ro3IfTmXyKh4VKk5Vi52+r9ZcHK00XVqRESkBSwG0RJ7e3v06tULvXr1AgDExMQgODgYz549w7t375CUlASZTAYbGxvY2tqiYsWKqFWrFiwsLNSe8+nTp1rJ3c/PD35+fnj79i0uXbqE0NBQJCUlwdzcHOXKlUO9evVQrlw5rcxFREREREREREREREREREREusViEB2xt7dHw4YN0bBhQ32norTixYujY8eO+k6DiIiIiIiIiIiIiIiIiIiINGCg7wSIiIiIiIiIiIiIiIiIiKhgWr9+PWQymdy/06dP6zutImfGjBmi21lbK0UUJXw8Ko+dQYiIiIiIiIiIiIiIiIiICjiZTKb0tgYGBrCxsYGdnR2KFSsGT09PeHt7o02bNihevLgOsySigoKdQYiIiIiIiIiIiIiIiIiIipCsrCzExsbi6dOnuHLlClasWIHBgwejXLly6Nu3L+7du6fvFIlIx1gMQkRERERERERERERERET0GUhLS8PWrVvh6emJ33//Xd/pEJEOcZkYIiIiIiIiIiIiIiIiIqJCyNraGgYG4vP/s7KykJCQoHC/1NRUjB8/HpGRkZg9e7YuUyQiPWFnECIiIiIiIiIiIiIiIiKiQigoKAixsbGif/Hx8UhPT0dISAiWLVsGNzc3yf3nzJmDrVu35nPWRJQfWAxCRERERERERERERERERFTEGBkZoXLlyhg9ejSCg4MxYcIEye1++OEHpKam5nN2lNOMGTMgCILcP1dXV32nRYUYi0GIiIiIiIiIiIiIiIiIiIowQ0ND/Pbbbxg+fLjouhcvXmD9+vX5nxQR6RSLQYiIiIiIiIiIiIiIiIiIPgO//fYbHBwcRPGDBw/qIRsi0iUWgxARERERERERERERERERACAtLQP7D1zBT9O3iK7r3H0exk38C/sPXEFaWoYesiNNWVlZoX///qL4mTNnkJmZqYeMiEhXjPSdABERERERERERERERERHpV3p6BlauOYYVq48hIiJOcpuQBy8R8uAltm4/i2LFbDFyWCuMHNYKxsY85FiY+Pn5YcmSJXKxhIQEvHv3DiVLltRo7JCQENy4cQOvXr1CWloanJycULJkSTRu3Bj29vYajV1QxMfH486dO3j06BHi4uKQkJAAY2NjWFhYwNHREa6urqhUqRKKFSum71SzPXz4EA8ePEBkZCQiIyORkZEBGxsblCxZElWrVoWbmxsMDQ01muP9+/fZ80RERCA+Ph4ymQwODg5wdHREjRo14ObmpqW/iJTBV2YiIiIiIiIiIiIiIiKiz1jIgxcYPW41gu48U3qfd+/iMHPOTuz79zKWLxkO98pldJghaVO5cuUk45GRkWoVg6SlpWHVqlVYunQpHj9+LLmNoaEhGjdujJkzZ6JJkyZKjduuXTscOnRILnb79m3UrFlT5Rw/1bt3b2zfvl0udu7cOTRu3FjhPqmpqVi/fj02bdqEixcvQhCEPOdxcXFBw4YN0alTJ3z55ZewtLTMdfsZM2bgl19+kYuFhYXB1dU1z7mkXLlyBStWrMB///2HFy9e5LqtjY0N/P390alTJ3Tv3h0WFhZ5ji8IAs6fP49Dhw7h9OnTuH79OjIycu8YVLx4cbRt2xaTJk1C1apVVfp7SHVcJoaIiIiIiIiIiIiIiIjoM3Xl6iO07ThbpUKQTwXdeYa2HWfjytVHWs6MdMXGxkYynpCQoPJYwcHB8PDwwDfffKOwEAQAMjMzcebMGfj6+mLMmDHIysrKc+xRo0aJYqtXr1Y5x09FRkZi7969crGqVavmWghy7tw5VK9eHSNHjsSFCxeUKgQBgGfPnmHbtm3o2bMnxowZo1Heqrh79y7atm2LevXqYf369XkWggAfup3s27cPgwYNQqlSpfDmzZtct9+6dSvKlSuHJk2aYP78+bh8+XKehSAA8PbtW6xbtw7Vq1fHoEGDkJycrPTfRapjMQgRERERERERERERERHRZyjkwQv06v8bEhJSNBonISEFvfr/hgcPX2opM9KluDjpZYBsbW1VGufatWto0KAB7t27p9J+y5cvx7Bhw/Lcrk2bNnBxcZGLbdmyBSkp6j9eN2zYgNTUVLnY8OHDFW5/5MgRtGzZMtdCF2UoW0CiqT179qB+/fo4cuSI2mPExcXh/fv3uW5z5coVpYpMFBEEARs2bECjRo3w9u1btceh3HGZGCIiIiIiIiIiIiIiIqLPTHp6BkaPW61xIchHCQkp+PqbVTh6YBqMjXkIsiALCwuTjDs5OSk9Rnh4OCZMmCBXWOLq6gp/f3+UKVMGlpaWePfuHc6fP48rV66IiiH+/vtvdOjQAR07dlQ4h4GBAUaMGIEpU6Zkx2JjY7Fjxw4MGjRI6Vw/tWbNGrnLZmZmGDBggOS2ERER6Nevn2RhROnSpdGoUSNUrFgRNjY2MDQ0RHx8PKKionD//n0EBQUhJiZGrRzV9eeff2LMmDGShSeGhobw8vKCp6cnnJ2dYW5ujtjYWLx8+RLXrl1DSEiIUt1aFDEwMECFChVQvXp1VKhQATY2NrC0tERSUhLevXuH27dvS3YPuXXrFvr27Yvjx4/DwIB9LLSNr8REREREREREREREREREn5mVa46pvTSMIkF3nmHlmmMY+/WXWh2XtCsgIEAUs7Ozg7Ozs9JjjB8/HlFRUQCAGjVqYOHChWjZsqXktoGBgejXrx9CQ0Pl4hMnTkSHDh0gk8kUzjN06FBMnz4d6enp2bHVq1erVQxy5swZPHjwQC7WrVs32NvbS27/22+/ITo6Wi5WqVIlLF++XOHf+pEgCLh69SoOHDiAv//+W+VcVXX27FmMGzdOVAhiYWGBb7/9FhMmTICjo6PC/d+9e4d//vkH69atw5UrV5Sa09DQEO3bt0eXLl3Qtm3bXMf/OMfy5cvx66+/yhXYnDx5EkuXLsW3336r1LykPJbXEBEREREREREREREREX1G0tIysHLNMZ2MvXLNMaSnZ+S9IelFfHw8Nm/eLIr7+fmp1JnhYyFI27ZtERgYmGtxRIMGDXDmzBk4ODjIxZ88eYLTp0/nOk+xYsXQpUsXuVhgYCDu3r2rdK4frV69WhQbMWKEwu13794td9nZ2Rnnz5/PsxAEAGQyGby9vTFr1iw8e/YMP/zwg8r5Kis2NhY9evQQdd0oV64crl27hjlz5uRZqFGsWDGMHDkSly9fxsmTJ2FnZ5fr9p07d0ZoaCj27t2L/v375zn+xzl++eUXnD9/XvRYWLRokSh/0hyLQYiIiIiIiIiIiIiIiIg+I0eO3cC7d3F5b6iGd+/icPjoDZ2MTZobM2YM4uPjRfH27durPFblypWxc+dOWFpa5rltmTJlMHPmTFF87969ee47atQoUUyqsCM30dHR2LNnj1ysatWqaNy4seT2aWlpePLkiVxs8ODBKF68uErzAoCRkRGqVKmi8n7KWrZsGd6+fSsXc3BwwPnz59Wa19/fP89iEF9fX5QrV07lsQHA09NTtFxPeHg4Dhw4oNZ4pBiLQYiIiIiIiIiIiIiIiIg+I6dO39Hp+AFndDs+qS41NRUjRozApk2bRNe5urqif//+Ko+5dOlSpQpBPurXrx/MzMzkYtevX89zP19fX1StWlUutnnzZrmlRvKyYcMGpKamysWGDRumcPvIyEhRrGLFikrPl1+Sk5OxZMkSUXzVqlUoW7asHjJSTpcuXVCpUiW5mNTyRaQZFoMQERERERERERERERERfUZuBz0t1ONT3rKyshAdHY2rV69i7ty5qFSpkmQ3DZlMht9++w3GxsYqje/u7q7UcimfsrW1Re3ateViQUFBSu07cuRIucsxMTHYuXOn0nPn7ERhZmaGAQMGKNzeyspKFAsLC1N6vvxy7NgxUeFKzZo10a1bNz1lpDxfX1+5y5cuXdJTJkUXi0GIiIiIiIiIiIiIiIiIPiNPQl/rdvwnb3Q6Pv2f8uXLQyaTif4ZGhrC0dER3t7emDJlCl68eCG5/5w5c9ClSxeV523RooVa+VarVk3ucmJiItLS0vLcb8CAAbCwsJCL5SzwUOT8+fMIDg6Wi3Xr1g0ODg4K97GxsUHJkiXlYqtWrcLjx4+VmjO/nD59WhTLWThTUJUoUULu8v379/WUSdHFYhAiIiIiIiIiIiIiIiKiz0hqaoZOx3+fmq7T8UlzlpaWWL16NX788Ue19vfw8FBrP3t7e1EsLi4uz/1sbW3Ru3dvuZhUkYcUqY4ow4cPz3O/Dh06yF2OiYlB3bp1MWfOHLx+rduCKmWdPXtWFGvatGm+5xETE4MNGzZg3Lhx8Pf3R4UKFeDs7AwzMzPJYiWZTIY5c+bIjZGUlIT0dL52aBOLQYiIiIiIiIiIiIiIiIg+I6amRjod38xUtSVHKP9YWlpi2LBhuH37NoYNG6b2OE5OTmrPn1NycrJS+44aNUoUkyr0+FRMTAx2794tF6tSpQp8fHzynO+HH34Q5RsXF4eff/4ZpUuXRv369TFlyhQcOXIEsbGxef8BOhAaGip32dbWFpUrV863+e/fv48uXbqgRIkSGDRoEJYuXYqAgACEhYUhMjISqampKo2nr9uxqNLtKz0RERERERERERERERERFSgVK5TEvfvPdTd+xRJ5b0RaYW1tDQMD8fn/BgYGsLa2hp2dHYoVKwYPDw94e3ujefPmsLW11XheKysrjcf4SBAEpbbz9PSEl5cXrl69mh3buHEj5s2bB1NTU8l9Nm3ahJSUFLmYMl1BgA9L8GzduhU9evQQFTUIgoDLly/j8uXLmDt3LmQyGWrUqAE/Pz+0aNECLVu2hImJiVLzqCs9PR3x8fFysRIlSkAmk+l03o9mzpyJWbNmISNDe52GlC0MIuWwGISIiIiIiIiIiIiIiIjoM1KrpqtOi0Fq1XTV2dgkLygoCK6urvpOI9+MGjVKrhgkOjoau3fvRt++fSW3X7NmjdxlMzMzDBgwQOn5OnTogIsXL+Lrr7/G5cuXFW4nCAKCgoIQFBSEpUuXwt7eHv3798cPP/yAUqVKKT2fKqKjo0UxOzs7ncyV08SJE7Fo0SKltjUyMoKZmRkMDQ3l4u/fv5cssiHt4TIxRERERERERERERERERJ8Rf78aOh2/qa9ux6fPV69evUQFD4qWirl48SLu3r0rF+vWrRscHBxUmtPDwwOXLl3CiRMn0K9fP6UKLmJiYrB06VJUrFgRy5YtU2m+gu7o0aOShSDm5ubo27cvVq1ahcuXL+PFixfIyMhAeno6EhISEBsbK/dv8uTJesj+88LOIERERERERERERERERESfkTatPFCsmC3evYvT+tjFitmibWsPrY9LBHwoOBg4cCCWLFmSHTt79iwePHiAypUry20rVSSi7BIxUpo3b47mzZsjKysLt27dwtmzZ3H+/HmcP38eb9++ldzn/fv3GDt2LN6+fYtZs2apPbcUqaKW2NhYrc4hZeLEiaJYly5dsGbNGpUKbZKSkrSZFklgZxAiIiIiIiIiIiIiIiKiz4iJiRFGDmulk7FHDmsFY2Oej066M3LkSFEsZ+FHXFwcdu7cKRerUqUKfHx8NJ7fwMAAHh4e+Pbbb7F79268efMGISEhWLRoEerXry+5z+zZsxEYGKjx3J8yNjaGjY2NXOzt27c6XWrl3r17uH//vlysQYMG2Llzp8odV6SWuSHtYjEIERERERERERERERER0Wdm5LBWqFnDRatj1qrpilHDW2t1TKKc3N3d0bRpU7nYxo0bkZqamn1506ZNSElJkdtGk64gealcuTLGjx+PwMBAXLhwARUrVhRts3DhQq3Pm3Oe2NhYPHz4UOvzfHTy5ElR7IcffoChoaHKY+kyT/qAxSBEREREREREREREREREnxljYyMsXzIc1tbmWhnPxsYCy5cMh5GR6geFiVQ1atQoucuRkZHYu3dv9uU1a9bIXW9mZoYBAwbkS24NGzbE0aNHYWJiIhf/77//tD5XkyZNRLGAgACtz/PRq1evRLGGDRuqPE5qaiquXr2qjZQoFywGISIiIiIiIiIiIiIiIvoMuVcug+2bJmpcEGJjY4FtGyeg8heltZQZUe46deqEEiVKyMU+LhVz+fJlBAUFyV3XtWtXlZc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",
      "text/plain": [
       "<Figure size 2200x1400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(11, 7), dpi=200)\n",
    "\n",
    "layer_labels = [(int(key.split(\":\")[0]), int(key.split(\":\")[1])) for key in bf_energies.keys()]\n",
    "plot_labels = [str(item) for item in layer_labels]\n",
    "\n",
    "plt.errorbar(\n",
    "    plot_labels,\n",
    "    sim_physical_energy_diff,\n",
    "    yerr=sim_physical_uncertainties.values(),\n",
    "    ecolor=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
    "    color=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
    "    capsize=4,\n",
    "    elinewidth=1.5,\n",
    "    fmt=\"o\",\n",
    "    markersize=8,\n",
    "    markeredgewidth=1,\n",
    "    label=\"Physical\",\n",
    ")\n",
    "\n",
    "plt.errorbar(\n",
    "    plot_labels,\n",
    "    sim_logical_energy_diff,\n",
    "    yerr=sim_logical_uncertainties.values(),\n",
    "    color=(0, 177 / 255.0, 152 / 255.0),\n",
    "    ecolor=(0, 177 / 255.0, 152 / 255.0),\n",
    "    capsize=4,\n",
    "    elinewidth=1.5,\n",
    "    fmt=\"o\",\n",
    "    markersize=8,\n",
    "    markeredgewidth=1,\n",
    "    label=\"Logical\",\n",
    ")\n",
    "\n",
    "ax.set_xlabel(\"Hamiltonian Parameters (U, V)\", fontsize=18)\n",
    "ax.set_ylabel(\"Energy above true ground state (in eV)\", fontsize=18)\n",
    "ax.set_title(\"CUDA-Q AIM Circuits Simulation (lower is better)\", fontsize=20)\n",
    "ax.legend(loc=\"upper right\", fontsize=18.5)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.yticks(fontsize=16)\n",
    "\n",
    "ax.axhline(y=0, color=\"black\", linestyle=\"--\", linewidth=2)\n",
    "plt.ylim(\n",
    "    top=max(sim_physical_energy_diff) + max(sim_physical_uncertainties.values()) + 0.2, bottom=-0.2\n",
    ")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running logical AIM on Infleqtion's hardware "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The entire workflow we've seen thus far can be seamlessly executed on real quantum hardware as well. CUDA-Q has integration with Infleqtion's gate-based neutral atom quantum computer, [Sqale](https://arxiv.org/html/2408.08288v2), allowing execution of CUDA-Q kernels on neutral-atom hardware via Infleqtion’s cross-platform Superstaq compiler API that performs low-level compilation and optimization under the hood. Indeed, the AIM research results seen in [our paper](https://arxiv.org/abs/2412.07670) were obtained via this complete end-to-end workflow.\n",
    "\n",
    "To do so, users can obtain a Superstaq API key from [superstaq.infleqtion.com](https://superstaq.infleqtion.com/) to gain access to Infleqtion's neutral-atom simulator, with [pre-registration](https://www.infleqtion.com/sqale-preregistration) open for access to Infleqtion’s neutral atom QPU."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a tutorial, let us reproduce the workflow we've run so far but on Infleqtion's QPU. We begin with the same GPU-enhanced VQE to generate the AIM circuits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "cudaq.reset_target()\n",
    "\n",
    "if cudaq.num_available_gpus() == 0:\n",
    "    cudaq.set_target(\"qpp-cpu\", option=\"fp64\")\n",
    "else:\n",
    "    cudaq.set_target(\"nvidia\", option=\"fp64\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computed optimal angles=[1.5846845738799267, 1.5707961678256028] for U=1, V=-9\n",
      "Computed optimal angles=[4.588033710930825, 4.712388365176642] for U=1, V=-1\n",
      "Computed optimal angles=[-1.588651490745171, 1.5707962742876598] for U=1, V=7\n",
      "Computed optimal angles=[1.64012940802256, 1.5707963354922125] for U=5, V=-9\n",
      "Computed optimal angles=[2.1293956916868737, 1.5707963294715355] for U=5, V=-1\n",
      "Computed optimal angles=[-1.6598458659836037, 1.570796331040382] for U=5, V=7\n",
      "Computed optimal angles=[1.695151467539617, 1.5707960973500679] for U=9, V=-9\n",
      "Computed optimal angles=[2.4149519241823376, 1.5707928509325972] for U=9, V=-1\n",
      "Computed optimal angles=[-1.7301462945564499, 1.570796044872433] for U=9, V=7\n",
      "\n",
      "Finished building optimized circuits!\n"
     ]
    }
   ],
   "source": [
    "device_circuit_dict = generate_circuit_set(\n",
    "    ignore_meas_id=True\n",
    ")  # Setting `ignore_meas_id=True` drops the noisy-identity gate from earlier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now, we change backends! Before selecting an Infleqtion machine in CUDA-Q, we must first set our Superstaq API key, like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# os.environ['SUPERSTAQ_API_KEY'] = \"api_key\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we declare the type of execution we would like on Infleqtion's machine based on the keyword options specified:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "cudaq.reset_target()\n",
    "\n",
    "# Set the following to run on Infleqtion's Sqale QPU:\n",
    "cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\")\n",
    "\n",
    "# Set the following to run an ideal dry-run on Infleqtion's Sqale QPU:\n",
    "# cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\", method=\"dry-run\")\n",
    "\n",
    "# Set the following to run a device-realistic noisy simulation of Infleqtion's Sqale QPU:\n",
    "# cudaq.set_target(\"infleqtion\", machine=\"cq_sqale_qpu\", method=\"noise-sim\")\n",
    "\n",
    "# Set the following to run a local, ideal emulation:\n",
    "# cudaq.set_target(\"infleqtion\", emulate=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With that, we're all set! That simple change instructs our AIM circuits to execute on Infleqtion's QPU (or simulator). Due to the general queue wait time of running on hardware, we optionally recommend enabling the `run_async=True` flag to asynchronously sample the circuits. This will allow the cell to be executed and not wait synchronously until all the jobs are complete, allowing other classical code to be run in the meantime. When using `run_async`, an optional directory to store the job information can be specified with `folder_path` (this will be important to later retrieve the job results from the same directory)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posting circuits associated with layer=('1:-9')\n",
      "Posting circuits associated with layer=('1:-1')\n",
      "Posting circuits associated with layer=('1:7')\n",
      "Posting circuits associated with layer=('5:-9')\n",
      "Posting circuits associated with layer=('5:-1')\n",
      "Posting circuits associated with layer=('5:7')\n",
      "Posting circuits associated with layer=('9:-9')\n",
      "Posting circuits associated with layer=('9:-1')\n",
      "Posting circuits associated with layer=('9:7')\n",
      "\n",
      "All circuits submitted for async sampling!\n"
     ]
    }
   ],
   "source": [
    "submit_aim_circuits(\n",
    "    device_circuit_dict, folder_path=\"hardware_aim_future_results\", shots_count=1000, run_async=True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the above cell execution, all the circuits will post to execute on QPU. We can then return at a later time to retrieve the job results with the cell below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Retrieving all circuits counts associated with layer=('1:-9')\n",
      "Retrieving all circuits counts associated with layer=('1:-1')\n",
      "Retrieving all circuits counts associated with layer=('1:7')\n",
      "Retrieving all circuits counts associated with layer=('5:-9')\n",
      "Retrieving all circuits counts associated with layer=('5:-1')\n",
      "Retrieving all circuits counts associated with layer=('5:7')\n",
      "Retrieving all circuits counts associated with layer=('9:-9')\n",
      "Retrieving all circuits counts associated with layer=('9:-1')\n",
      "Retrieving all circuits counts associated with layer=('9:7')\n",
      "\n",
      "Obtained all circuit samples!\n"
     ]
    }
   ],
   "source": [
    "aim_device_data = _get_async_results(circuit_layers, folder_path=\"hardware_aim_future_results\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "physical_energies, physical_uncertainties = aim_physical_energies(\n",
    "    data_ordering, aim_device_data[\"physical\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "logical_energies, logical_uncertainties = aim_logical_energies(\n",
    "    data_ordering, aim_device_data[\"logical\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer=(1, -9) has brute-force energy of: -18.251736027394713\n",
      "Physical circuit of layer=(1, -9) got an energy of: -17.626499999999997\n",
      "Logical circuit of layer=(1, -9) got an energy of: -17.69666562801761\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(1, -1) has brute-force energy of: -2.265564437074638\n",
      "Physical circuit of layer=(1, -1) got an energy of: -2.1415\n",
      "Logical circuit of layer=(1, -1) got an energy of: -2.2032104443266585\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(1, 7) has brute-force energy of: -14.252231964940428\n",
      "Physical circuit of layer=(1, 7) got an energy of: -12.9955\n",
      "Logical circuit of layer=(1, 7) got an energy of: -13.76919450035401\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, -9) has brute-force energy of: -19.293350575766127\n",
      "Physical circuit of layer=(5, -9) got an energy of: -18.331\n",
      "Logical circuit of layer=(5, -9) got an energy of: -18.85730052910377\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, -1) has brute-force energy of: -3.608495283014149\n",
      "Physical circuit of layer=(5, -1) got an energy of: -3.476\n",
      "Logical circuit of layer=(5, -1) got an energy of: -3.5425689231532203\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(5, 7) has brute-force energy of: -15.305692796870582\n",
      "Physical circuit of layer=(5, 7) got an energy of: -14.043500000000002\n",
      "Logical circuit of layer=(5, 7) got an energy of: -14.795918428433312\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, -9) has brute-force energy of: -20.39007993367173\n",
      "Physical circuit of layer=(9, -9) got an energy of: -19.4715\n",
      "Logical circuit of layer=(9, -9) got an energy of: -19.96524696701215\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, -1) has brute-force energy of: -5.260398644698076\n",
      "Physical circuit of layer=(9, -1) got an energy of: -4.973\n",
      "Logical circuit of layer=(9, -1) got an energy of: -5.207315773582224\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n",
      "Layer=(9, 7) has brute-force energy of: -16.429650912487233\n",
      "Physical circuit of layer=(9, 7) got an energy of: -15.182\n",
      "Logical circuit of layer=(9, 7) got an energy of: -16.241375689575516\n",
      "------------------------------------------------------------------------\n",
      "Logical circuit achieved the lower energy!\n",
      "------------------------------------------------------------------------ \n",
      "\n"
     ]
    }
   ],
   "source": [
    "physical_energy_diff, logical_energy_diff = _get_energy_diff(\n",
    "    bf_energies, physical_energies, logical_energies\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before, we use the same metric of comparing against the true ground state energies; however, this time, both the physical and logical circuits are fully exposed to real hardware noise. Yet, we expect the use of logical qubits afforded to us by the `[[4,2,2]]` code to achieve energies closer to the true ground state than the bare physical circuits (up to a certain error threshold). And indeed they do! Visually, we can plot the energy deviations of both the physical and logical circuits from the cell above and observe that the logical circuits are able to outperform the physical circuits by obtaining much lower energies, demonstrating the power of error detection and the beginning possibilities of fault-tolerant quantum computation: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2200x1400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(11, 7), dpi=200)\n",
    "\n",
    "plt.errorbar(\n",
    "    plot_labels,\n",
    "    physical_energy_diff,\n",
    "    yerr=physical_uncertainties.values(),\n",
    "    ecolor=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
    "    color=(20 / 255.0, 26 / 255.0, 94 / 255.0),\n",
    "    capsize=4,\n",
    "    elinewidth=1.5,\n",
    "    fmt=\"o\",\n",
    "    markersize=8,\n",
    "    markeredgewidth=1,\n",
    "    label=\"Physical\",\n",
    ")\n",
    "plt.errorbar(\n",
    "    plot_labels,\n",
    "    logical_energy_diff,\n",
    "    yerr=logical_uncertainties.values(),\n",
    "    color=(0, 177 / 255.0, 152 / 255.0),\n",
    "    ecolor=(0, 177 / 255.0, 152 / 255.0),\n",
    "    capsize=4,\n",
    "    elinewidth=1.5,\n",
    "    fmt=\"o\",\n",
    "    markersize=8,\n",
    "    markeredgewidth=1,\n",
    "    label=\"Logical\",\n",
    ")\n",
    "\n",
    "ax.set_xlabel(\"Hamiltonian Parameters (U, V)\", fontsize=18)\n",
    "ax.set_ylabel(\"Energy above true ground state (in eV)\", fontsize=18)\n",
    "ax.set_title(\"CUDA-Q AIM Infleqtion Hardware Execution (lower is better)\", fontsize=20)\n",
    "ax.legend(loc=\"upper left\", fontsize=18.5)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.yticks(fontsize=16)\n",
    "\n",
    "ax.axhline(y=0, color=\"black\", linestyle=\"--\", linewidth=2)\n",
    "plt.ylim(top=max(physical_energy_diff) + max(physical_uncertainties.values()) + 0.2, bottom=-0.2)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
